Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Localized Basis for Effective Lattice Hamiltonians Lattice Wannier Functions
Rabe, K M
1994-01-01
A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrTiO_3$, the Jahn-Teller instability in $La_{1-x}(Ca,Sr,Ba)_xMnO_3$ and the antiferroelectric transition in $PbZrO_3$ are discussed. For the oxygen- octahedron rotation transition in $SrTiO_3$, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corres...
Hamiltonian for the Zeros of the Riemann Zeta Function.
Bender, Carl M; Brody, Dorje C; Müller, Markus P
2017-03-31
A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of H[over ^] are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that H[over ^] is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.
Lattice effects on Laughlin wave functions and parent Hamiltonians
Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.
2016-12-01
We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.
MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR HAMILTONIAN SYSTEM
JIANGQIBAO; HANMAOAN
1999-01-01
In this paper, Melnikov functions which apper in the study of limit cycles of a perturbed planar Hamiltonlan system are studied. There are two main contributions here. The first one is related to the explicit formulae for these functions: a new method is developed to achieve the goal for the second one (Theorem A). the authors also discover a close relation between Melnlkov functions and focal qtmntities (Theorem 13). This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function (see §5). I)espite these results, this paper also includes other related resuEs, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system.
Energy-Based Lyapunov Functions for Forced Hamiltonian Systems with Dissipation
Maschke, Bernhard; Ortega, Romeo; Schaft, Arjan J. van der
2000-01-01
In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network
Energy-Based Lyapunov Functions for Forced Hamiltonian Systems with Dissipation
Maschke, Bernhard; Ortega, Romeo; Schaft, Arjan J. van der
2000-01-01
In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network
Ramezanpour, A.
2016-06-01
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Function group approach to unconstrained Hamiltonian Yang-Mills theory
Salmela, A
2004-01-01
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.
On critical points for noncoercive functionals and subharmonic solutions of some Hamiltonian systems
Klaus Schmitt
2000-10-01
Full Text Available The paper is concerned with existence results about subharmonic solutions of some Hamiltonian systems. The existence of such solutions is established using a variational approach and results about minima of noncoercive functionals.
Hydrodynamic Covariant Symplectic Structure from Bilinear Hamiltonian Functions
Capozziello S.
2005-07-01
Full Text Available Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of motion directly related to a hydrodynamic picture. This feature is gauge free and it seems a deep link common to all interactions, electromagnetism and gravity included. This scheme could lead toward a full canonical quantization.
Feedback control of nonlinear differential algebraic systems using Hamiltonian function method
LIU Yanhong; LI Chunwen; WU Rebing
2006-01-01
The stabilization and H∞ control of nonlinear differential algebraic systems (NDAS) are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization (DHR) structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.
无
2010-01-01
The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging method.First,a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay.Then,stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system,and after that the Lyapunov function of the averaged It? equation is taken as the optimal linear combination of the corresponding independent first integrals in involution.Finally,the stability of the system is determined by using the largest eigenvalue of the linearized system.Two examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.
Nomura, K; Otsuka, T; Shimizu, N; Vretenar, D
2011-01-01
Microscopic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing an accurate global description of nuclear ground states and collective excitations. For spectroscopic applications this framework has to be extended to account for collective correlations related to restoration of symmetries broken by the static mean field, and for fluctuations of collective variables. In this work we compare two approaches to five-dimensional quadrupole dynamics: the collective Hamiltonian for quadrupole vibrations and rotations, and the Interacting Boson Model. The two models are compared in a study of the evolution of non-axial shapes in Pt isotopes. Starting from the binding energy surfaces of $^{192,194,196}$Pt, calculated with a microscopic energy density functional, we analyze the resulting low-energy collective spectra obtained from the collective Hamiltonian, and the corresponding IBM-2 Hamiltonian. The calculated excitation spectra and transition probabilities for t...
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Nechaev, I. A.; Krasovskii, E. E.
2016-11-01
We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.
吴颖; 罗亚军; 杨晓雪
2003-01-01
We present a novel formalism for energy eigenvalue problems when the corresponding Hamiltonians can be expressed as a function of an angular momentum. The problems are turned into finding operator polynomials by solving a c-number differential equation. Simple and efficient computer-aided analytical and numerical methods may be developed based on the formalism.
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
Computing the real-time Green's Functions of large Hamiltonian matrices
Iitaka, T
1996-01-01
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method to condensed matter physics will be found in H. Tanaka, Phys. PRB 57, 2168 (1998).
Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
Kominis, Y; Hizanidis, K [School of Electrical and Computer Engineering, National Technical University of Athens, Association EURATOM-Hellenic Republic, Zographou GR-15773 (Greece); Constantinescu, D [Department of Applied Mathematics, University of Craiova, A I Cuza Street 13, Craiova 1100, 200585 Romania (Romania); Dumbrajs, O [Department of Engineering Physics and Mathematics, Helsinki University of Technology, Association EURATOM-TEKES, FIN-02150 Espoo (Finland)
2008-03-21
The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincare surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of the system.
Optimal trajectory planning based on Hamiltonian function of a spherical mobile robot
Chen Ming; Zhan Qiang; Liu Zengbo; Cai Yao
2008-01-01
Designed for planetary exploration, a spherical mobile robot BHQ-1 was briefly introduced.The motion model of BHQ-1 was established and quasi-velocities were introduced to simplify some dynamic quantities.Based on the model, the time- and energy-based optimal trajectory of BHQ-1 was planned with Hamiltonian function.The effects of three key coefficients on the shape and direction of the planned trajectory were discussed by simulations.Experimental result of the robot ability in avoiding an obstacle was presented to validate the trajectory planning method.
Parry, A. O.; Boulter, C. J.
1995-02-01
We study the pair correlation function for an inhomogeneous fluid or Ising-type spin system near a wall with particular attention to the complete wetting phase transition. We show that one can unify a generalized interfacial Hamiltonian theory with a mean-field treatment of correlations provided we follow a systematic scheme for reconstructing order-parameter fluctuations. Near a complete wetting transition it is necessary to use a model effective Hamiltonian HI(2) [ l1, l2] which is a functional of two collective coordinates in order to properly describe the coupling between fluctuations near the wall and the depinning fluid (αβ) interface. This gives an accurate description of the Ornstein-Zernike-like fluctuations of particles located near the αβ interface and the non-Ornstein-Zernike behavior of correlations near the wall. We show that the off-diagonal elements of the stiffness matrix characterizing HI(2) [ l1, l2] are related to singular behaviour of the free-energy.
Cohen, D; Kottos, T
2001-03-01
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a two-dimensional well, and x is a parameter. By changing x we can deform the "shape" of the well. The quantum eigenstates of the system are /n(x)>. We analyze numerically how the parametric kernel P(n/m)=//(2) evolves as a function of delta(x)[triple bond](x-x(0)). This kernel, regarded as a function of n-m, characterizes the shape of the wave functions, and it also can be interpreted as the local density of states. The kernel P(n/m) has a well-defined classical limit, and the study addresses the issue of quantum-classical correspondence. Both the perturbative and the nonperturbative regimes are explored. The limitations of the random matrix theory approach are demonstrated.
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Schwörer, Magnus; Breitenfeld, Benedikt; Tröster, Philipp; Bauer, Sebastian; Lorenzen, Konstantin; Tavan, Paul; Mathias, Gerald
2013-06-28
Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.
Oh, Yong-Geun
2012-01-01
The main purpose of this note is to rectify the incomplete proof given in arXiv:1111.5992 of the following result, when $\\dim M = 2$. High dimensional cases will be treated elsewhere: For any \\emph{contractible topological Hamiltonian loop} $\\phi_F$, $$ f_{\\underline{\\mathbb F}} \\equiv 0, \\quad \\mathbb F(t,x,y) := F(t,x) $$ where $f_{\\underline{\\mathbb F}} := \\lim_{i \\to \\infty} f_{\\underline{\\mathbb F_i}}$ for an approximating sequence $F_i$ of $F$. Here $f_{\\underline{\\mathbb F_i}}$ is the basic phase function of the Lagrangian submanifold $\\phi_{\\mathbb F_i}^1(o_\\Delta) = \\Graph \\phi_{F_i}^1$ which is the graph selector previously constructed by Lagrangian Floer theory. A complete revision of the paper "Homotopy invariance of spectral invariants of topological Hamiltonian flows and its Lagrangian analog" in dimension 2, which combines Part I of arXiv:1111.5992(v5) and this note, is available in the author's homepage (http://www.math.wisc.edu/~oh/preprints.html).
Moretti, Valter
2016-01-01
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by A.M. Gleason to prove his celebrated theorem. In particular, the problem of associating quantum state with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical observables representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical objects representing quantum ones result to be frame functions. The requirements of $U(n)$ covariance and (convex) linearity play a central r\\^ole in the proof of those theorems. A new characterization of classical observables describing quantum observables is presented, together with a geometric description of the ...
Shujuan LI; Yuzhen WANG
2006-01-01
Based on Hamiltonian formulation, this paper proposes a design approach to nonlinear feedback excitation control of synchronous generators with steam valve control, disturbances and unknown parameters. It is shown that the dynamics of the synchronous generators can be expressed as a dissipative Hamiltonian system, based on which an adaptive H-infinity controller is then designed for the systems by using the structure properties of dissipative Hamiltonian systems.Simulations show that the controller obtained in this paper is very effective.
Siminovitch, David; Untidt, Thomas; Nielsen, Niels Chr
2004-01-01
Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker-Campbell-Hausdorff problem for SU(N) systems from Nfunction. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester's theorem (also known as the spectral theorem) and the EEHT expansion.
Ryan, M.
1972-01-01
The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.
Berg, J. S. [Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.
2015-05-03
I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.
Krishnamurthy, Srini; Van Orden, Derek; Yu, Zhi-Gang
2016-09-01
We have developed a hybrid method that can be applied to study isolated defects in semiconductor compounds and superlattices. The method is a combination of (1) a long-range tight-binding (TB) Hamiltonian, (2) a first-principles Hamiltonian, and (3) a Green's function (GF) formalism. The calculation of the GF requires accurate energy band structure, wave functions, and defect potentials. The TB Hamiltonian with sp 3 orbitals basis ensures accurate band gaps and band masses while providing the functional form for the wave functions. We calculated the band gaps of InAs/GaSb and InAs/InAsSb strained-layer superlattices and found them to agree well with measurements. The change in potentials caused by native point defects (NPDs) was obtained from a first-principles method using Spanish Initiative for Electronic Simulations with Thousands of Atoms, which also uses sp 3 basis. We describe the method of calculating NPD energy levels in compounds and superlattices, obtain some defect levels in GaAs, InAs, InSb, and GaSb compounds, and provide details of the NPD-level calculations.
Mehta, Dhagash; Kastner, Michael
2011-06-01
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.
Exploring the Hamiltonian inversion landscape.
Donovan, Ashley; Rabitz, Herschel
2014-08-07
The identification of quantum system Hamiltonians through the use of experimental data remains an important research goal. Seeking a Hamiltonian that is consistent with experimental measurements constitutes an excursion over a Hamiltonian inversion landscape, which is the quality of reproducing the data as a function of the Hamiltonian parameters. Recent theoretical work showed that with sufficient experimental data there should be local convexity about the true Hamiltonian on the landscape. The present paper builds on this result and performs simulations to test whether such convexity is observed. A gradient-based Hamiltonian search algorithm is incorporated into an inversion routine as a means to explore the local inversion landscape. The simulations consider idealized noise-free as well as noise-ridden experimental data. The results suggest that a sizable convex domain exists about the true Hamiltonian, even with a modest amount of experimental data and in the presence of a reasonable level of noise.
Hamiltonian description of the ideal fluid
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems.
Orsucci, Davide [Scuola Normale Superiore, I-56126 Pisa (Italy); Burgarth, Daniel [Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom); Facchi, Paolo; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Nakazato, Hiromichi; Yuasa, Kazuya [Department of Physics, Waseda University, Tokyo 169-8555 (Japan); Giovannetti, Vittorio [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
2015-12-15
The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of lik
Nomura, K; Rodriguez-Guzman, R; Robledo, L M; Sarriguren, P
2010-01-01
Spectroscopic calculations are carried out, for the description of the shape/phase transition in Pt nuclei in terms of the Interacting Boson Model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density dependent Gogny-D1S Energy Density Functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. Using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and side-band levels are well reproduced. From the ...
Mochon, C
2006-01-01
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.
Vilasi, Gaetano
2001-01-01
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m
Dai Haitao; Cheng Wei; Li Mingzhi
2008-01-01
The 3-dimensional couple equations of magneto-electro-elastic structures are derived under Hamiltonian system based on the Hamilton principle. The problem of single sort of variables is converted into the problem of double sorts of variables, and the Hamilton canonical equations are established. The 3-dimensional problem of magneto-electro-elastic structure which is investigated in Euclidean space commonly is converted into symplectic system. At the same time the Lagrange system is converted into Hamiltonlan system. As an example, the dynamic characteristics of the simply supported functionally graded magneto-electro-elastic material (FGMM) plate and pipe are investigated. Finally, the problem is solved by symplectic algorithm. The results show that the physical quantifies of displace-ment, electric potential and magnetic potential etc. change continuously at the interfaces between layers under the transverse pressure while some other physical quantifies such as the stress, electric and magnetic displacement are not continuous. The dynamic stiffness is increased by the piezoelectric effect while decreased by the piezomagnetic effect.
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Rañada, Manuel F.
2017-08-01
The existence of quasi-bi-Hamiltonian structures for the Tremblay-Turbiner-Winternitz (TTW) and the Post-Winternitz (PW) systems is studied. We first recall that the superintegrability of these two systems is related with the existence of certain complex functions endowed with interesting Poisson bracket properties, and then we prove the existence of several quasi-bi-Hamiltonian structures making use of these complex functions. This is done in two steps: first with complex 2-forms (wedge product of the differentials of the complex functions) and then with several real 2-forms. The properties of these geometric structures and the associated recursion operators are also analyzed. The paper can be considered as divided in two parts. In the first part a we study the TTW system (related to the harmonic oscillator) and in the second part we study the PW system (related to the Kepler problem).
Continuum Hamiltonian Hopf Bifurcation II
Hagstrom, G I
2013-01-01
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (HH) bifurcation. Necessary notions pertaining to spectra, structural stability, signature of the continuous spectra, and normal forms are described. The theory developed is applicable to a wide class of 2+1 noncanonical Hamiltonian matter models, but the specific example of the Vlasov-Poisson system linearized about homogeneous (spatially independent) equilibria is treated in detail. For this example, structural (in)stability is established in an appropriate functional analytic setting, and two kinds of bifurcations are considered, one at infinite and one at finite wavenumber. After defining and describing the notion of dynamical accessibility, Kre\\u{i}n-like the...
Brugnano, Luigi; Trigiante, Donato
2009-01-01
One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that standard (even symplectic) methods can only exactly preserve quadratic Hamiltonians. In this paper, a new family of methods, called Hamiltonian Boundary Value Methods (HBVMs), is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, perfectly $A$-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María; Głazek, Stanisław D.
2016-07-01
We derive asymptotic freedom of gluons in terms of the renormalized SU(3) Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of g up to third order. The resulting three-gluon vertex is a function of the scale parameter s that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian {β} -function coincides with the one obtained in an earlier calculation using a different generator.
Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin
2016-09-01
We apply broken-symmetry density functional theory to determine isotropic exchange-coupling constants and local zero-field splitting (ZFS) tensors for the tetragonal Mn12(t)BuAc single-molecule magnet. The obtained parametrization of the many-spin Hamiltonian (MSH), taking into account all 12 spin centers, is assessed by comparing theoretical predictions for thermodynamic and spectroscopic properties with available experimental data. The magnetic susceptibility (calculated by the finite-temperature Lanczos method) is well approximated, and the intermultiplet excitation spectrum from inelastic neutron scattering (INS) experiments is correctly reproduced. In these respects, the present parametrization of the 12-spin model represents a significant improvement over previous theoretical estimates of exchange-coupling constants in Mn12, and additionally offers a refined interpretation of INS spectra. Treating anisotropic interactions at the third order of perturbation theory, the MSH is mapped onto the giant-spin Hamiltonian describing the S = 10 ground multiplet. Although the agreement with high-field EPR experiments is not perfect, the results clearly point in the right direction and for the first time rationalize the angular dependence of the transverse-field spectra from a fully microscopic viewpoint. Importantly, transverse anisotropy of the effective S = 10 manifold is explicitly shown to arise largely from the ZFS-induced mixing of exchange multiplets. This effect is given a thorough analysis in the approximate D2d spin-permutational symmetry group of the exchange Hamiltonian.
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
The electronic Hamiltonian for cuprates
Annett, James F.; Mcmahan, A. K.; Martin, Richard M.
1991-01-01
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
刘艳红; 李春文; 王玉振
2009-01-01
Using the Hamiltonian function method, we investigate the excitation control of multi-machine multi-load power systems presented by nonlinear differential algebraic equations. First, the power system is reformulated as a novel Hamiltonian realization structure via pre-feedback state control. Then, based on the dissipative Hamiltonian realization of the system, a decentralized nonlinear excitation control scheme is constructed. The stability of the closed loop system is analyzed as well. The proposed strategy takes advantage of the intrinsic properties especially including the internal power balance of the power system. Simulation illustrates the effectiveness of the control strategy.
Equivalence of Conformal Superalgebras to Hamiltonian Superoperators
Xiaoping Xu
2001-01-01
In this paper, we present a formal variational calculus of super functions in one real variable and find the conditions for a "matrix differential operator'' to be a Hamiltonian superoperator. Moreover, we prove that conformal superalgebras are equivalent to certain Hamiltonian superoperators.
Bohr Hamiltonian with time-dependent potential
Naderi, L.; Hassanabadi, H.; Sobhani, H.
2016-04-01
In this paper, Bohr Hamiltonian has been studied with the time-dependent potential. Using the Lewis-Riesenfeld dynamical invariant method appropriate dynamical invariant for this Hamiltonian has been constructed and the exact time-dependent wave functions of such a system have been derived due to this dynamical invariant.
Momentum and hamiltonian in complex action theory
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
Unified Hamiltonian for conducting polymers
Leitão Botelho, André; Shin, Yongwoo; Li, Minghai; Jiang, Lili; Lin, Xi
2011-11-01
Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ɛ specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.
Hamiltonian systems as selfdual equations
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
M Talebian; E Talebian; A Abdi
2012-05-01
We obtained an approximation of the force ﬁeld of -quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals 19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals 18, 231 (1991)] in 6−311+G(2d) basis set for H16Si7O6 cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir;
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...... results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions....
EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS
Yuqian GUO; Daizhan CHENG
2006-01-01
In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Baykara, N. A. [Marmara University, Faculty of Sciences and Letters, Mathematics Department, Göztepe Campus, 34730, Istanbul (Turkey)
2015-12-31
Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.
Maxwell's Optics Symplectic Hamiltonian
Kulyabov, D S; Sevastyanov, L A
2015-01-01
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. This allows to use a symplectic Hamiltonian formalism. The proposed formalism will be used by the authors in the future to justify the methods of vector bundles (Hamiltonian bundles) in transformation optics.
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Garrido, L. M.; Pascual, P.
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Paul, Arpita; Sun, Jianwei; Perdew, John P.; Waghmare, Umesh V.
2017-02-01
While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in BaTiO3, PbTiO3, and KNbO3, quantitative estimates of the transition temperatures (TC) suffer from errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of BaTiO3, PbTiO3, and KNbO3 obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of TC, which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in TC originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of BaTiO3, PbTiO3, and KNbO3. We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.
Minimal Realizations of Supersymmetry for Matrix Hamiltonians
Andrianov, Alexandr A
2014-01-01
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.
Path Integrals and Hamiltonians
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Asymptocic Freedom of Gluons in Hamiltonian Dynamics
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom of gluons in terms of the renormalized $SU(3)$ Yang-Mills Hamiltonian in the Fock space. Namely, we use the renormalization group procedure for effective particles (RGPEP) to calculate the three-gluon interaction term in the front-form Yang-Mills Hamiltonian using a perturbative expansion in powers of $g$ up to third order. The resulting three-gluon vertex is a function of the scale parameter $s$ that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant exhibits asymptotic freedom, and the corresponding Hamiltonian $\\beta$-function coincides with the one obtained in an earlier calculation using a different generator.
Running Couplings in Hamiltonians
Glazek, S D
2000-01-01
We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.
Covariant Hamiltonian field theory
Giachetta, G; Sardanashvily, G
1999-01-01
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The main peculiarity of these Hamilton equations lies in the fact that, for degenerate systems, they contain additional gauge fixing conditions. We develop the BRST extension of the covariant Hamiltonian formalism, characterized by a Lie superalgebra of BRST and anti-BRST symmetries.
Hamiltonian dynamics of extended objects
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi; Nielsen, Holger Bech
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.
Telesca, R.; Bolink, H.; Yunoki, S.; Hadziioannou, G.; Duijnen, P.Th. van; Snijders, J.G.; Jonkman, H.T.; Sawatzky, G.A.
2001-01-01
We present density-functional and time-dependent density-functional studies of the ground, ionic, and excited states of a series of oligomers of thiophene. We show that, for the physical properties, the most relevant highest occupied and lowest unoccupied molecular orbitals develop gradually from mo
Minimal realizations of supersymmetry for matrix Hamiltonians
Andrianov, Alexander A., E-mail: andrianov@icc.ub.edu; Sokolov, Andrey V., E-mail: avs_avs@rambler.ru
2015-02-06
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of 2×2 matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated. - Highlights: • Weak and strong minimization of a matrix intertwining operator. • Criterion of strong minimizability from the right of a matrix intertwining operator. • Conditions of existence of a constant symmetry matrix for a matrix Hamiltonian. • Method of constructing of a matrix Hamiltonian with a given constant symmetry matrix. • Examples of constructing of 2×2 matrix Hamiltonians with a given symmetry matrix.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENG Daizhan; XI Zairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonian realizatiou. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural outpnt. Then some conditions for an affine nonlinear system to have a Hamiltonian realization arc given.For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.
FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS
CHENGDaizhan; XIZairong
2002-01-01
This paper investigates the relationship between state feedback and Hamiltonican realization.Firest,it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization.Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output.Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given.some conditions for an affine nonlinear system to have a Hamiltonian realization are given.For generalized outputs,the conditions of the feedback,keeping Hamiltonian,are discussed.Finally,the admissible feedback controls for generalized Hamiltonian systems are considered.
A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION
丰建文; 陈士华
2001-01-01
This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.
Remarks on hamiltonian digraphs
Gutin, Gregory; Yeo, Anders
2001-01-01
This note is motivated by A.Kemnitz and B.Greger, Congr. Numer. 130 (1998)127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-locally semicomplete digraphs by Bang-Jensen, Huang, and Prisner, J. Combin. Theory...... of Fan's su#cient condition [5] for an undirected graph to be hamiltonian. In this note we give another, more striking, example of this kind, which disproves a conjecture from [6]. We also show that the main result of [6] 1 is an easy consequence of the characterization of hamiltonian out......-tournaments by Bang-Jensen, Huang and Prisner [4]. For further information and references on hamiltonian digraphs, see e.g. the chapter on hamiltonicity in [1] as well as recent survey papers [2, 8]. We use the standard terminology and notation on digraphs as described in [1]. A digraph D has vertex set V (D) and arc...
Microscopic plasma Hamiltonian
Peng, Y.-K. M.
1974-01-01
A Hamiltonian for the microscopic plasma model is derived from the Low Lagrangian after the dual roles of the generalized variables are taken into account. The resulting Hamilton equations are shown to agree with the Euler-Lagrange equations of the Low Lagrangian.
Monte Carlo Hamiltonian: Linear Potentials
LUO Xiang-Qian; LIU Jin-Jiang; HUANG Chun-Qing; JIANG Jun-Qin; Helmut KROGER
2002-01-01
We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
New approaches to generalized Hamiltonian realization of autonomous nonlinear systems
王玉振; 李春文; 程代展
2003-01-01
The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally,this paper proposes several sufficient conditions for feedback dissipative realization.
On Hamiltonian realization of time-varying nonlinear systems
无
2007-01-01
This paper Investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a nonsingular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
Hamiltonian Description of Multi-fluid Streaming
Valls, C.; de La Llave, R.; Morrison, P. J.
2001-10-01
The general noncanonical Hamiltonian description of interpenetrating fluids coupled by electrostatic, gravitational, or other forces is presented. This formalism is used to describe equilibrium and nonlinear stability using techniques of Hamiltonian dynamics theory. For example, we study the stability of two warm counter-streaming electron beams in a neutralizing ion background. The normal modes are obtained from an energy functional by computing the lowest-order expression for the perturbed energy about an equilibrium, and transforming the corresponding system into action-angle variables. Higher-order terms in the Hamiltonian provide coupling between normal modes and can lead to instability because of the presence of negative energy modes (NEM's). (The signature of the NEM's is determined by the signature of the Hamiltonian, Moser's bracket definition, or the conventional plasma definition in terms of the dielectric function, all of which are shown to be equivalent.) The possible nonlinear behavior is discovered by constructing the Birkhoff normal form. Accounting for resonances, we transform away terms in the Hamiltonian to address the question of long-time stability for such systems.
Hamiltonian description of closed configurations of the vacuum magnetic field
Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru [National Research Centre Kurchatov Institute (Russian Federation)
2015-05-15
Methods of obtaining and using the Hamiltonians of closed vacuum magnetic configurations of fusion research systems are reviewed. Various approaches to calculate the flux functions determining the Hamiltonian are discussed. It is shown that the Hamiltonian description allows one not only to reproduce all traditional results, but also to study the behavior of magnetic field lines by using the theory of dynamic systems. The potentialities of the Hamiltonian formalism and its close relation to traditional methods are demonstrated using a large number of classical examples adopted from the fundamental works by A.I. Morozov, L.S. Solov’ev, and V.D. Shafranov.
Darboux transformations of the Jaynes-Cummings Hamiltonian
Samsonov, B F; Samsonov, Boris F; Negro, Javier
2004-01-01
A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schr\\"odinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.
Bountis, Tassos
2012-01-01
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...
Wieland, Wolfgang M
2013-01-01
This paper presents a Hamiltonian formulation of spinfoam-gravity, which leads to a straight-forward canonical quantisation. To begin with, we derive a continuum action adapted to the simplicial decomposition. The equations of motion admit a Hamiltonian formulation, allowing us to perform the constraint analysis. We do not find any secondary constraints, but only get restrictions on the Lagrange multipliers enforcing the reality conditions. This comes as a surprise. In the continuum theory, the reality conditions are preserved in time, only if the torsionless condition (a secondary constraint) holds true. Studying an additional conservation law for each spinfoam vertex, we discuss the issue of torsion and argue that spinfoam gravity may indeed miss an additional constraint. Next, we canonically quantise. Transition amplitudes match the EPRL (Engle--Pereira--Rovelli--Livine) model, the only difference being the additional torsional constraint affecting the vertex amplitude.
Quantum Hamiltonian Complexity
2014-01-01
Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a "Quantum Cook-Levin Theorem" to deep insights into the structure of 1D low-temperature quantum systems via s...
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions
Qi Wang
2013-01-01
Full Text Available By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.
An intuitive Hamiltonian for quantum search
Fenner, S A
2000-01-01
We present new intuition behind Grover's quantum search algorithm by means of a Hamiltonian. Given a black-box Boolean function f mapping strings of length n into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that w can also be found in the same amount time by letting the quantum system evolve according to a simple Hamiltonian depending only on f. Their system evolves along a path far from that taken by Grover's original algorithm, however. The current paper presents an equally simple Hamiltonian matching Grover's algorithm step for step. The new Hamiltonian is similar in appearance from that of Farhi & Gutmann, but has some important differences, and provides new intuition for Grover's algorithm itself. This intuition both contrasts with and supplements other explanations of Grover's algorithm as a rotation in two dimensions, and suggests that the Hamiltonian-based approach to quantum algorithms can ...
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurelien; Blumberger, Jochen; Elstner, Marcus
2016-10-11
In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated p-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.
Gillet, Natacha; Berstis, Laura; Wu, Xiaojing; Gajdos, Fruzsina; Heck, Alexander; de la Lande, Aurélien; Blumberger, Jochen; Elstner, Marcus
2016-10-11
In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.
Position-dependent mass quantum Hamiltonians: general approach and duality
Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.
2016-03-01
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.
Equivalent Hamiltonians with additional discrete states
Chinn, C.R. (Physics Department, Lawrence Livermore National Laboratory, Livermore, CA (USA)); Thaler, R.M. (Los Alamos National Laboratory, Los Alamos, NM (USA) Department of Physics, Case Western Reserve University, Cleveland, OH (USA))
1991-01-01
Given a particular Hamiltonian {ital H}, we present a method to generate a new Hamiltonian {ital {tilde H}}, which has the same discrete energy eigenvalues and the same continuum phase shifts as {ital H}, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian {ital h}{sub 1}, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Equivalent Hamiltonians with additional discrete states
Chinn, C. R.; Thaler, R. M.
1991-01-01
Given a particular Hamiltonian H, we present a method to generate a new Hamiltonian H~, which has the same discrete energy eigenvalues and the same continuum phase shifts as H, but which also has additional given discrete eigenstates. This method is used to generate a Hamiltonian h1, which gives rise to a complete orthonormal set of basis states, which contain a given set of biorthonormal discrete states, the continuum states of which are asymptotic to plane waves (have zero phase shifts). Such a set of states may be helpful in representing the medium modification of the Green's function due to the Pauli principle, as well as including Pauli exclusion effects into scattering calculations.
Hamiltonian Dynamics of Cosmological Quintessence Models
Ivanov, Rossen I
2016-01-01
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any pos...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2016-01-01
We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian $H_s$, which is a matrix written in a basis that depend on the scale (or size) parameter $s$. The effective Hamiltonians $H_s$ and the (regularized) canonical Hamiltonian $H_{0}$ are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Hou, Yusheng; Xiang, Hongjun; Gong, Xingao; Key Laboratory of Computational Physical Sciences (Ministry of Education) Collaboration
Based on the density functional theory and our new model Hamiltonian, we have studied the basal-plane antiferromagnetism in the novel Jeff = 1/2 Mott insulator Ba2IrO4. By comparing the magnetic properties of the bulk Ba2IrO4 with those of the single-layer Ba2IrO4, we demonstrate unambiguously that the basal-plane antiferromagnetism is caused by the intralyer magnetic interactions rather than by the previously proposed interlayer ones. In order to reveal the origin of the basal-plane antiferromagnetism, we propose a new model Hamiltonian by adding the single ion anisotropy and pseudo-quadrupole interactions into the general bilinear pseudo-spin Hamiltonian. The obtained magnetic interaction parameters indicate that the single ion anisotropy and pseudo-quadrupole interactions are unexpectedly strong. Systematical Monte Carlo simulations demonstrate that the basal-plane antiferromagnetism is caused by the isotropic Heisenberg, bond-dependent Kitaev and pseudo-quadrupole interactions. Our results show for the first time that the single ion anisotropy and pseudo-quadrupole interaction can play significant roles in establishing the exotic magnetism in the Jeff = 1/2 Mott insulator.
An underlying geometrical manifold for Hamiltonian mechanics
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar
2016-06-15
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Chromatic roots and hamiltonian paths
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Momentum and Hamiltonian in Complex Action Theory
Nagao, Keiichi
2011-01-01
In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view. In arXiv:1104.3381[quant-ph], introducing a philosophy to keep the analyticity in parameter variables of FPI and defining a modified set of complex conjugate, hermitian conjugates and bras, we have extended $| q >$ and $| p >$ to complex $q$ and $p$ so that we can deal with a complex coordinate $q$ and a complex momentum $p$. After reviewing them briefly, we describe in terms of the newly introduced devices the time development of a $\\xi$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum again via the saddle point for $p$. This study confirms that the momentum and Hamiltonian in the CAT have t...
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G; Sardanashvily, G
2007-01-01
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian completely integrable Hamiltonian system.
Quantum control by means of hamiltonian structure manipulation.
Donovan, A; Beltrani, V; Rabitz, H
2011-04-28
A traditional quantum optimal control experiment begins with a specific physical system and seeks an optimal time-dependent field to steer the evolution towards a target observable value. In a more general framework, the Hamiltonian structure may also be manipulated when the material or molecular 'stockroom' is accessible as a part of the controls. The current work takes a step in this direction by considering the converse of the normal perspective to now start with a specific fixed field and employ the system's time-independent Hamiltonian structure as the control to identify an optimal form. The Hamiltonian structure control variables are taken as the system energies and transition dipole matrix elements. An analysis is presented of the Hamiltonian structure control landscape, defined by the observable as a function of the Hamiltonian structure. A proof of system controllability is provided, showing the existence of a Hamiltonian structure that yields an arbitrary unitary transformation when working with virtually any field. The landscape analysis shows that there are no suboptimal traps (i.e., local extrema) for controllable quantum systems when unconstrained structural controls are utilized to optimize a state-to-state transition probability. This analysis is corroborated by numerical simulations on model multilevel systems. The search effort to reach the top of the Hamiltonian structure landscape is found to be nearly invariant to system dimension. A control mechanism analysis is performed, showing a wide variety of behavior for different systems at the top of the Hamiltonian structure landscape. It is also shown that reducing the number of available Hamiltonian structure controls, thus constraining the system, does not always prevent reaching the landscape top. The results from this work lay a foundation for considering the laboratory implementation of optimal Hamiltonian structure manipulation for seeking the best control performance, especially with limited
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamilton-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical pictu...
On the Reaction Path Hamiltonian
孙家钟; 李泽生
1994-01-01
A vector-fiber bundle structure of the reaction path Hamiltonian, which has been introduced by Miller, Handy and Adams, is explored with respect to molecular vibrations orthogonal to the reaction path. The symmetry of the fiber bundle is characterized by the real orthogonal group O(3N- 7) for the dynamical system with N atoms. Under the action of group O(3N- 7). the kinetic energy of the reaction path Hamiltonian is left invariant. Furthermore , the invariant behaviour of the Hamiltonian vector fields is investigated.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Estimation of a general time-dependent Hamiltonian for a single qubit.
de Clercq, L E; Oswald, R; Flühmann, C; Keitch, B; Kienzler, D; Lo, H-Y; Marinelli, M; Nadlinger, D; Negnevitsky, V; Home, J P
2016-04-14
The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.
Kuramoto dynamics in Hamiltonian systems.
Witthaut, Dirk; Timme, Marc
2014-09-01
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We show that locking of the phase of one oscillator on a Kuramoto manifold to the average phase emerges where the transverse Hamiltonian action dynamics of that specific oscillator becomes unstable. Moreover, the inverse participation ratio of the Hamiltonian dynamics perturbed off the manifold indicates the global synchronization transition point for finite N more precisely than the standard Kuramoto order parameter. The uncovered Kuramoto dynamics in Hamiltonian systems thus distinctly links dissipative to conservative dynamics.
Hamiltonian Structure of PI Hierarchy
Kanehisa Takasaki
2007-03-01
Full Text Available The string equation of type (2,2g+1 may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself.
Alternative Hamiltonian representation for gravity
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems
Szederkenyi, Gabor; Hangos, Katalin M
2004-04-26
We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.
Hamiltonian analysis of interacting fluids
Banerjee, Rabin; Mitra, Arpan Krishna [S. N. Bose National Centre for Basic Sciences, Kolkata (India); Ghosh, Subir [Indian Statistical Institute, Kolkata (India)
2015-05-15
Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical (Noether) stress tensor and the symmetric one obtained by metric variation are discussed. (orig.)
When are vector fields hamiltonian?
Crehan, P
1994-01-01
Dynamical systems can be quantised only if they are Hamiltonian. This prompts the question from which our talk gets its title. We show how the simple predator-prey equation and the damped harmonic oscillator can be considered to be Hamiltonian with respect to an infinite number of non-standard Poisson brackets. This raises some interesting questions about the nature of quantisation. Questions which are valid even for flows which possess a canonical structure.
Elementary Quantum Gates Based on Intrinsic Interaction Hamiltonian
CHEN Jing; YU Chang-Shui; SONG He-Shan
2006-01-01
A kind of new operators, the generalized pseudo-spin operators are introduced and a universal intrinsic Hamiltonian of two-qubit interaction is studied in terms of the generalized pseudo-spin operators. A fundamental quantum gate U(θ) is constructed based on the universal Hamiltonian and shown that the roles of the new quantum gate U(θ) is equivalent, functionally, to the joint operation of Hadamard and C-Not gates.
Smooth prime integrals for quasi-integrable Hamiltonian systems
Chierchia, L.; Gallavotti, G. (Rome Univ. (Italy). Ist. di Matematica)
1982-02-11
A Hamiltonian with N degrees of freedom, analytic perturbation of a canonically integrable strictly nonisochronous analytic Hamiltonian, is considered. We show the existence of N functions on phase space and of class Csup(infinity) which are prime integrals for the perturbed motions on a suitable region whose Lebesgue measure tends to fill locally the phase space as the perturbation's magnitude approaches zero. An application to the perturbations of isochronous nonresonant linear oscillators is given.
Hernández, P; Peña, C; Torro, E; Wennekers, J; Wittig, H
2008-01-01
A new method to determine the low-energy couplings of the $\\Delta S=1$ weak Hamiltonian is presented. It relies on a matching of the topological poles in $1/m^2$ of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the $\\epsilon$-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU(4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.
Interchange graphs and the Hamiltonian cycle polytope
Sierksma, G
1998-01-01
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge di
Hamiltonian approach to hybrid plasma models
Tronci, Cesare
2010-01-01
The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.
Redesign of the DFT/MRCI Hamiltonian.
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
Hou, Y. S.; Xiang, H. J.; Gong, X. G.
2016-04-01
Based on the density functional theory and model Hamiltonian, we studied the basal-plane antiferromagnetism in the spin-orbit Mott insulator Ba2IrO4. By comparing the magnetic properties of the bulk Ba2IrO4 with those of the single-layer Ba2IrO4, we demonstrate unambiguously that the basal-plane antiferromagnetism is caused by the intralyer magnetic interactions rather than by the previously proposed interlayer ones. Aiming at revealing the origin of the basal-plane antiferromagnetism, we add the single ion anisotropy and pseudo-quadrupole interactions into the general bilinear pseudo-spin Hamiltonian. The obtained magnetic interaction parameters indicate that the single ion anisotropy and pseudo-quadrupole interactions are unexpectedly strong. Systematical Monte Carlo simulations demonstrate that the basal-plane antiferromagnetism is caused by isotropic Heisenberg, bond-dependent Kitaev and pseudo-quadrupole interactions. On the basis of this study the single ion anisotropy and pseudo-quadrupole interactions could play a role in explaining magnetic interactions in other iridates.
Hamiltonian thermodynamics of three-dimensional dilatonic black hole
Dias, Gonçalo A S
2008-01-01
The action for a class of three-dimensional dilaton-gravity theories with a cosmological constant can be recast in a Brans-Dicke type action, with its free $\\omega$ parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ($\\omega\\to\\infty$), a dimensionally reduced cylindrical four-dimensional general relativity theory ($\\omega=0$), and a theory representing a class of theories ($\\omega=-3$). The Hamiltonian formalism is setup in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unc...
Study on the stability of switched dissipative Hamiltonian systems
ZHU Liying; WANG Yuzhen
2006-01-01
The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.
The rovibrational Hamiltonian for ammonia-like molecules.
Makarewicz, Jan; Skalozub, Alexander
2002-03-01
A new exact quantum mechanical rovibrational Hamiltonian operator for ammonia-like molecules is derived. The Hamiltonian is constructed in a molecular system of axes, such that its z' axis makes a trisection of the pyramidal angle formed by three bond vectors with the vertex on the central atom. The introduced set of the internal rovibrational coordinates is adapted to facilitate a convenient description of the inversion motion. These internal coordinates and the molecular axis system have a remarkable property, namely, the internal vibrational angular momentum of the molecule equals zero. This property significantly reduces the Coriolis coupling and simplifies the form of the Hamiltonian. The correctness of this Hamiltonian is proved by a numerical procedure. The orthogonal Radau vectors allowing us to define a similar molecular axis system and the internal coordinates are considered. The Hamiltonian for the Radau parameterization takes a form simple enough to carry out effectively variational calculations of the molecular rovibrational states. Under the appropriate choice of the variational basis functions, the Hamiltonian matrix elements are fully factorizable and do not have any singularities. A convenient method of symmetrization of the basis functions is proposed.
Reinforcement learning for port-hamiltonian systems.
Sprangers, Olivier; Babuška, Robert; Nageshrao, Subramanya P; Lopes, Gabriel A D
2015-05-01
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning (RL) approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust. The parameters of the control law are found by using actor-critic (AC) RL, enabling the search for near-optimal control policies satisfying a desired closed-loop energy landscape. The advantage is that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the RL perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the AC framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
Effective Hamiltonian of strained graphene.
Linnik, T L
2012-05-23
Based on the symmetry properties of the graphene lattice, we derive the effective Hamiltonian of graphene under spatially nonuniform acoustic and optical strains. Comparison with the published results of the first-principles calculations allows us to determine the values of some Hamiltonian parameters, and suggests the validity of the derived Hamiltonian for acoustical strain up to 10%. The results are generalized for the case of graphene with broken plane reflection symmetry, which corresponds, for example, to the case of graphene placed on a substrate. Here, essential modifications to the Hamiltonian give rise, in particular, to the gap opening in the spectrum in the presence of the out-of-plane component of optical strain, which is shown to be due to the lifting of the sublattice symmetry. The developed effective Hamiltonian can be used as a convenient tool for analysis of a variety of strain-related effects, including electron-phonon interaction or pseudo-magnetic fields induced by the nonuniform strain.
Dyson--Schwinger Approach to Hamiltonian QCD
Campagnari, Davide R; Huber, Markus Q; Vastag, Peter; Ebadati, Ehsan
2016-01-01
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By means of the DSEs the various $n$-point functions, needed in expectation values of observables like the Hamilton operator, can be thus expressed in terms of the variational kernels of our trial ansatz. Equations of motion for these variational kernels are derived by minimizing the energy density and solved numerically.
Hamiltonian Dynamics of Preferential Attachment
Zuev, Konstantin; Krioukov, Dmitri
2015-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton's equations. We derive the explicit form of the Hamiltonian that governs network growth in preferential attachment. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by preferential attachment is nearly identical to the ensemble of random graphs with scale-free degree d...
First principles of Hamiltonian medicine.
Crespi, Bernard; Foster, Kevin; Úbeda, Francisco
2014-05-19
We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.
Recent advances in the numerical solution of Hamiltonian partial differential equations
Barletti, Luigi; Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice
2016-10-01
In this paper, we study recent results in the numerical solution of Hamiltonian partial differential equations (PDEs), by means of energy-conserving methods in the class of Line Integral Methods, in particular, the Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). We show that the use of energy-conserving methods, able to conserve a discrete counterpart of the Hamiltonian functional (which derives from a proper space semi-discretization), confers more robustness to the numerical solution of such problems.
Skurnick, Ronald; Davi, Charles; Skurnick, Mia
2005-01-01
Since 1952, several well-known graph theorists have proven numerous results regarding Hamiltonian graphs. In fact, many elementary graph theory textbooks contain the theorems of Ore, Bondy and Chvatal, Chvatal and Erdos, Posa, and Dirac, to name a few. In this note, the authors state and prove some propositions of their own concerning Hamiltonian…
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Maslov index for Hamiltonian systems
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
Dynamical stability of Hamiltonian systems
无
2000-01-01
Dynamical stability has become the center of study on Hamiltonian system. In this article we intro-duce the recent development in some areas closely related to this topic, such as the KAM theory, Mather theory, Arnolddiffusion and non-singular collision of n-body problem.
Derivation of Hamiltonians for accelerators
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Time-reversible Hamiltonian systems
Schaft, Arjan van der
1982-01-01
It is shown that transfer matrices satisfying G(-s) = G(s) = G^T(-s) have a minimal Hamiltonian realization with an energy which is the sum of potential and kinetic energy, yielding the time reversibility of the equations. Furthermore connections are made with an associated gradient system. The
Connecting orbits for families of Tonelli Hamiltonians
Mandorino, Vito
2011-01-01
We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the time-one maps of a family of Tonelli Hamiltonians. Such systems are known as 'polysystems' or 'iterated function systems'. When specialized to families of twist maps on the cylinder, our results are similar to those obtained by Moeckel [20] and Le Calvez [15]. Our approach is based on weak KAM theory and is close to the one used by Bernard in [3] to study the case of a single Tonell...
Subsystem's dynamics under random Hamiltonian evolution
Vinayak,
2011-01-01
We study time evolution of a subsystem's density matrix under a unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian. We exactly calculate all coherences, purity and fluctuations. The reduced density matrix is described in terms of a noncentral correlated Wishart ensemble. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.
On third order integrable vector Hamiltonian equations
Meshkov, A. G.; Sokolov, V. V.
2017-03-01
A complete list of third order vector Hamiltonian equations with the Hamiltonian operator Dx having an infinite series of higher conservation laws is presented. A new vector integrable equation on the sphere is found.
Hamiltonian realizations of nonlinear adjoint operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2002-01-01
This paper addresses the issue of state-space realizations for nonlinear adjoint operators. In particular, the relationships between nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are established. Then, characterizations of the adjoints of control
Hamiltonian Realizations of Nonlinear Adjoint Operators
Fujimoto, Kenji; Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel ope
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Quantization of noncommutative completely integrable Hamiltonian systems
Giachetta, G. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Mangiarotti, L. [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino (Italy); Sardanashvily, G. [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)]. E-mail: gennadi.sardanashvily@unicam.it
2007-02-26
Integrals of motion of a Hamiltonian system need not commute. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as the Abelian one.
Port-Hamiltonian systems: an introductory survey
Schaft, van der Arjan; Sanz-Sole, M.; Soria, J.; Varona, J.L.; Verdera, J.
2006-01-01
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian
New sufficient conditions for Hamiltonian paths.
Rahman, M Sohel; Kaykobad, M; Firoz, Jesun Sahariar
2014-01-01
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Geometric Hamiltonian structures and perturbation theory
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Driving Hamiltonian in a Quantum Search Problem
Oshima, K
2001-01-01
We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> $ from an initial state $|s>$, the driving Hamiltonian $E^{\\prime}|s> < s|(E^{\\prime} \
Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology
Pinaki Patra
2014-01-01
Full Text Available The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense Lagrangian. We have used this method for the Regge-Teitelboim (RT minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.
2016-03-01
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael; Guzmán, María José
2016-11-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudoinverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first-class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms and the (local) Lorentz transformations of the vielbein. In particular, the Arnowitt, Deser, and Misner algebra of general relativity is recovered as a subalgebra.
On Hamiltonian formulation of cosmologies
K D Krori; S Dutta
2000-03-01
Novello et al [1,2] have shown that it is possible to ﬁnd a pair of canonically conjugate variables (written in terms of gauge-invariant variables) so as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW cosmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrödinger wave equation has been derived and exact solutions have been worked out for the stiff matter era for some cosmological models. It is argued that these solutions appear to hint at their possible relevance in the early phase of cosmological evolution.
A Hamiltonian approach to Thermodynamics
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Hamiltonian formulation of teleparallel gravity
Ferraro, Rafael
2016-01-01
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Hamiltonian chaos and fractional dynamics
Zaslavsky, George M
2008-01-01
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image ...
LIMIT CYCLES OF SOME Z3-EQUIVARIANT NEAR-HAMILTONIAN SYSTEMS OF DEGREES 3 AND 4
Hongyan Ma; Maoan Han; Christoph Lhotka
2009-01-01
This paper studies the number of limit cycles of some Z3-equivariant near-Hamiltonian systems of degrees 3 and 4, which arc a perturbation of a cubic Hamiltonian system. By the Melnikov function method, we obtain 5 and 6 limit cycles respectively.
Action-angle coordinates for time-dependent completely integrable Hamiltonian systems
Giachetta, Giovanni; Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mails: giovanni.giachetta@unicam.it; luigi.mangiarotti@unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
2002-07-26
A time-dependent completely integrable Hamiltonian system is proved to admit the action-angle coordinates around any instantly compact regular invariant manifold. Written relative to these coordinates, its Hamiltonian and first integrals are functions only of action coordinates. (author). Letter-to-the-editor.
Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.
Yang, Yongliang; Wunsch, Donald; Yin, Yixin
2017-02-01
This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
Sheftel, M. B.; Yazıcı, D.; Malykh, A. A.
2017-06-01
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian structures of the two-component general heavenly system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We discover that in the two-component form we have only a single nonlocal recursion operator. Composing the recursion operator with the first Hamiltonian operator we obtain second Hamiltonian operator. We check the Jacobi identities for the second Hamiltonian operator and compatibility of the two Hamiltonian structures using P. Olver's theory of functional multi-vectors. Our well-founded conjecture is that P. Olver's method works fine for nonlocal operators. We show that the general heavenly equation in the two-component form is a bi-Hamiltonian system integrable in the sense of Magri. We demonstrate how to obtain nonlocal Hamiltonian flows generated by local Hamiltonians by using formal adjoint recursion operator.
Nonclassical degrees of freedom in the Riemann Hamiltonian.
Srednicki, Mark
2011-09-02
The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
Bounded stabilisation of stochastic port-Hamiltonian systems
Satoh, Satoshi; Saeki, Masami
2014-08-01
This paper proposes a stochastic bounded stabilisation method for a class of stochastic port-Hamiltonian systems. Both full-actuated and underactuated mechanical systems in the presence of noise are considered in this class. The proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability. The bounded region and achieving probability are both assignable, and a stochastic Lyapunov function is explicitly provided based on a Hamiltonian structure. Although many conventional stabilisation methods assume that the noise vanishes at the origin, the proposed method is applicable to systems under persistent disturbances.
A parity breaking Ising chain Hamiltonian as a Brownian motor
Cornu, F.; Hilhorst, H. J.
2014-10-01
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian {\\cal H} =-{U_2}\\sumk sksk+1 - {U_3}\\sumk sksk+1sk+3 and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio {U_3}/{U_2} and of the conserved magnetization M=\\sum_ksk . The symmetry of the U3 term in the Hamiltonian is discussed.
The Hamilton-Jacobi method and Hamiltonian maps
Abdullaev, S.S. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, Juelich (Germany)
2002-03-29
A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method. (author)
The Hamilton-Jacobi method and Hamiltonian maps
Abdullaev, S. S.
2002-03-01
A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method.
NATO Advanced Study Institute on Hamiltonian Dynamical Systems and Applications
2008-01-01
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems as well as the theory of Hamiltonian systems in infinite dimensional phase space; these are described in depth in this volume. Applications are also presented to several important areas of research, including problems in classical mechanics, continu...
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise; Sotiriadis, Spyros
2016-08-01
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Cluster expansion for ground states of local Hamiltonians
Bastianello, Alvise, E-mail: abastia@sissa.it [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Sotiriadis, Spyros [SISSA, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Institut de Mathématiques de Marseille (I2M), Aix Marseille Université, CNRS, Centrale Marseille, UMR 7373, 39, rue F. Joliot Curie, 13453, Marseille (France); University of Roma Tre, Department of Mathematics and Physics, L.go S.L. Murialdo 1, 00146 Roma (Italy)
2016-08-15
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Bender, C M; Chen, J H; Jones, H F; Milton, K A; Ogilvie, M C; Bender, Carl M.; Brody, Dorje C.; Chen, Jun-Hua; Jones, Hugh F.; Milton, Kimball A.; Ogilvie, Michael C.
2006-01-01
In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian $\\cP\\cT$-symmetric wrong-sign quartic Hamiltonian $H=\\half p^2-gx^4$ has the same spectrum as the conventional Hermitian Hamiltonian $\\tilde H=\\half p^2+4g x^4-\\sqrt{2g} x$. Here, this equivalence is demonstrated very simply by means of differential-equation techniques and, more importantly, by means of functional-integration techniques. It is shown that the linear term in the Hermitian Hamiltonian is anomalous; that is, this linear term has no classical analog. The anomaly arises because of the broken parity symmetry of the original non-Hermitian $\\cP\\cT$-symmetric Hamiltonian. This anomaly in the Hermitian form of a $\\cP\\cT$-symmetric quartic Hamiltonian is unchanged if a harmonic term is introduced into $H$. When there is a harmonic term, an immediate physical consequence of the anomaly is the appearance of bound states; if there were no anomaly term, there would be no bound states. Possible extensions of this work to...
Historical Hamiltonian Dynamics: symplectic and covariant
Lachieze-Rey, M
2016-01-01
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field theories on space-time. It is based on the notion of (Hamiltonian) histories, which are sections of the (extended) phase space bundle. It is developed in the space of sections, in contradistinction with the usual formalism which works in the bundle manifold. In field theories, the formalism remains covariant and does not require a spitting of space-time. It considers space-time exactly in the same manner than time in usual dynamics, both being particular cases of the evolution domain. It applies without modification when the histories (the fields) are forms rather than scalar functions, like in electromagnetism or in tetrad general relativity. We develop a differential calculus in the infinite dimensional space of histories. It admits a (generalized) symplectic form which d...
Spectrum of an Elliptic Free Fermionic Corner Transfer Matrix Hamiltonian
Cuerno, R
1993-01-01
The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic $R$ matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.
Hamiltonian indices and rational spectral densities
Byrnes, C. I.; Duncan, T. E.
1980-01-01
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
LOCALIZATION THEOREM ON HAMILTONIAN GRAPHS
无
2000-01-01
Let G be a 2-connected graph of order n( 3).If I(u,v) S(u,v) or max {d(u),d(v)} n/2 for any two vertices u,v at distance two in an induced subgraph K1,3 or P3 of G,then G is hamiltonian.Here I(u,v) = ｜N(u)∩ N(v)｜,S(u,v) denotes thenumber of edges of maximum star containing u,v as an induced subgraph in G.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Chasing Hamiltonian structure in gyrokinetic theory
Burby, J W
2015-01-01
Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a \\emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Hamiltonian cosmology in bigravity and massive gravity
Soloviev, Vladimir O
2015-01-01
In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in solving other problems. The purpose of this work is to give an introduction both to the Hamiltonian formalism and to the cosmology of bigravity. We sketch three roads to the Hamiltonian of bigravity with the dRGT potential: the metric, the tetrad and the minisuperspace approaches.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
Nonperturbative light-front Hamiltonian methods
Hiller, J R
2016-01-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli--Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, $\\phi^4$ theory, ordinary Yukawa theory, supersymmetric Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations...
Fourier series expansion for nonlinear Hamiltonian oscillators.
Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac
2010-06-01
The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Using Hamiltonian control to desynchronize Kuramoto oscillators
Gjata, Oltiana; Asllani, Malbor; Barletti, Luigi; Carletti, Timoteo
2017-02-01
Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.
Hamiltonian description of composite fermions: Magnetoexciton dispersions
Murthy, Ganpathy
1999-11-01
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in fractional quantum hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the ν=13, 25, and 37 gapped fractions, and find approximate agreement with numerical results. I also analyze the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 25 and 37, and it is shown that the spin-polarized 25 state, in contrast to the spin-polarized 13 state, cannot be described as a simple quantum ferromagnet.
Hamiltonian formalism and path entropy maximization
Davis, Sergio; González, Diego
2015-10-01
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the second law of thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the second law is a fundamental property of plausible inference.
Nonperturbative light-front Hamiltonian methods
Hiller, J. R.
2016-09-01
We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.
Entanglement Concentration with Quantum Non Demolition Hamiltonians
Tatham, Richard
2011-01-01
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
A Hamiltonian method for finding broadband modal eigenvalues.
Wang, Haozhong; Wang, Ning; Gao, Dazhi
2012-02-01
For shallow water waveguides over a layered elastic bottom, modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of π [C. T. Tindle and N. R. Chapman, J. Acoust. Soc. Am. 96, 1777-1782 (1994)]. In this paper, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. The Hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the Pekeris waveguide with fluid/elastic bottoms. For each proper or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually. The Hamiltonian method shows good performance by comparing with KRAKEN.
Adapted Su-Schrieffer-Heeger Hamiltonian for polypyrrole
Li, Minghai; Lin, Xi
2010-10-01
A generic class of Hamiltonians based on the Su-Schrieffer-Heeger (SSH) model is introduced to address the material-specific properties of conducting polymers beyond polyacetylene. Two physical parameters are incorporated into the original SSH model Hamiltonian, one being the scaling parameter γ accounts for the modified electron-phonon coupling strength of aromatic rings and the other parameter ɛ representing the attractive cores of heterogeneous atoms, such as NH, S, and O. Their values are uniquely determined by two independent measurements, such as the experimental band gap of bulk polypyrrole (PPy) and the dimerization amplitude of pyrrole monomer computed by ab initio coupled cluster methods as chosen in this work. With the optimized values of {γ=1.46,ɛ=4.27eV} , the adapted SSH (aSSH) Hamiltonian accurately reproduces the band gaps, molecular geometries, quasiparticle energies and wave functions, order parameters, discretized phonons around nonlinear polarons, and infrared and Raman spectra of both neutral and p -doped PPy chains of all lengths. It is expected that the generic formalism of the aSSH Hamiltonian, equipped with their corresponding {γ,ɛ} values, would be applicable to other conducting polymers, such as polythiophene, polyfuran, poly-( p -phenylene-vinylene), polyaniline, and their functional derivatives.
The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
Lee, Yng-Ing
2010-01-01
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They can be considered as a generalization of special Lagrangians or Lagrangian and minimal submanifolds. Joyce, Schoen and the author show that given any compact rigid Hamiltonian stationary Lagrangian in $\\C^n$, one can always find a family of Hamiltonian stationary Lagrangians of the same type in any compact symplectic manifolds with a compatible metric. The advantage of this result is that it holds in very general classes. But the disadvantage is that we do not know where these examples locate and examples in this family might be far apart. In this paper, we derive a local condition on Kahler manifolds which ensures the existence of one family of Hamiltonian stationary Lagrangian tori near a point with given frame satisfying the criterion. Butscher and Corvino ever proposed a condition in n=2. But our condition appears to be different from theirs. The condition d...
Singh, Parampreet
2015-01-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum ...
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Roychoudhury, Rajkumar
2011-01-01
The generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason for this anomaly is discussed in the frame work of position dependent mass models by choosing $A(x)$ as the inverse square root of the mass function.
Spectral Invariants in Rabinowitz Floer homology and Global Hamiltonian perturbations
Albers, Peter
2010-01-01
Spectral invariant were introduced in Hamiltonian Floer homology by Viterbo, Oh, and Schwarz. We extend this concept to Rabinowitz Floer homology. As an application we derive new quantitative existence results for leaf-wise intersections. The importance of spectral invariants for the presented application is that spectral invariants allow us to derive existence of critical points of the Rabinowitz action functional even in degenerate situations where the functional is not Morse.
Implicit variational principle for contact Hamiltonian systems
Wang, Kaizhi; Wang, Lin; Yan, Jun
2017-02-01
We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form α =\\text{d}u-p\\text{d}x under Tonelli and Lipschitz continuity conditions.
Some Graphs Containing Unique Hamiltonian Cycles
Lynch, Mark A. M.
2002-01-01
In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…
A parcel formulation for Hamiltonian layer models
Bokhove, O.; Oliver, M.
2009-01-01
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamilton
ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS
QI Zhao-hui(齐朝晖); Alexander P. Seyranian
2002-01-01
The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Hamiltonian for a restricted isoenergetic thermostat
Dettmann, C. P.
1999-01-01
Nonequilibrium molecular dynamics simulations often use mechanisms called thermostats to regulate the temperature. A Hamiltonian is presented for the case of the isoenergetic (constant internal energy) thermostat corresponding to a tunable isokinetic (constant kinetic energy) thermostat, for which a Hamiltonian has recently been given.
Normal Form for Families of Hamiltonian Systems
Zhi Guo WANG
2007-01-01
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d+1. And some dynamical consequences are obtained.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
Square conservation systems and Hamiltonian systems
王斌; 曾庆存; 季仲贞
1995-01-01
The internal and external relationships between the square conservation scheme and the symplectic scheme are revealed by a careful study on the interrelation between the square conservation system and the Hamiltonian system in the linear situation, thus laying a theoretical basis for the application and extension of symplectic schemes to square conservations systems, and of those schemes with quadratic conservation properties to Hamiltonian systems.
A Hamiltonian approach to Thermodynamics
Baldiotti, M C; Molina, C
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed ontop of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.
Model spin-orbit coupling Hamiltonians for graphene systems
Kochan, Denis; Irmer, Susanne; Fabian, Jaroslav
2017-04-01
We present a detailed theoretical study of effective spin-orbit coupling (SOC) Hamiltonians for graphene-based systems, covering global effects such as proximity to substrates and local SOC effects resulting, for example, from dilute adsorbate functionalization. Our approach combines group theory and tight-binding descriptions. We consider structures with global point group symmetries D6 h, D3 d, D3 h, C6 v, and C3 v that represent, for example, pristine graphene, graphene miniripple, planar boron nitride, graphene on a substrate, and free standing graphone, respectively. The presence of certain spin-orbit coupling parameters is correlated with the absence of the specific point group symmetries. Especially in the case of C6 v—graphene on a substrate, or transverse electric field—we point out the presence of a third SOC parameter, besides the conventional intrinsic and Rashba contributions, thus far neglected in literature. For all global structures we provide effective SOC Hamiltonians both in the local atomic and Bloch forms. Dilute adsorbate coverage results in the local point group symmetries C6 v, C3 v, and C2 v, which represent the stable adsorption at hollow, top and bridge positions, respectively. For each configuration we provide effective SOC Hamiltonians in the atomic orbital basis that respect local symmetries. In addition to giving specific analytic expressions for model SOC Hamiltonians, we also present general (no-go) arguments about the absence of certain SOC terms.
Effective Hamiltonians for Complexes of Unstable Particles
Urbanowski, K
2014-01-01
Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \\rightarrow \\infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\\rightarrow \\infty$.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Simulating sparse Hamiltonians with star decompositions
Childs, Andrew M
2010-01-01
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts, this algorithm uses (d^2(d+log* N)||H||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||H||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
Poincare algebra realized in Hamiltonian formalism of the Relativistic Theory of Gravitation
Soloviev, V O
2010-01-01
We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in accordance with the fact that RTG has 10 integrals of motion.
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Struckmeier, Jürgen; Vasak, David
2016-01-01
We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether's theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether's theorem. The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the Hamiltonian.
Full hamiltonian structure for a parametric coupled Korteweg-de Vries system
Restuccia, A
2014-01-01
We obtain the full hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system.
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
van Oers, Alexander M.; Maas, Leo R. M.; Bokhove, Onno
2017-02-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.
Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems
Starkov, Konstantin E. [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)], E-mail: konst@citedi.mx
2008-10-06
In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.
Lectures on Hamiltonian Dynamics : Theory and Applications
Benettin, Giancarlo; Kuksin, Sergei
2005-01-01
This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Extended Hamiltonian approach to continuous tempering.
Gobbo, Gianpaolo; Leimkuhler, Benedict J
2015-06-01
We introduce an enhanced sampling simulation technique based on continuous tempering, i.e., on continuously varying the temperature of the system under investigation. Our approach is mathematically straightforward, being based on an extended Hamiltonian formulation in which an auxiliary degree of freedom, determining the effective temperature, is coupled to the physical system. The physical system and its temperature evolve continuously in time according to the equations of motion derived from the extended Hamiltonian. Due to the Hamiltonian structure, it is easy to show that a particular subset of the configurations of the extended system is distributed according to the canonical ensemble for the physical system at the correct physical temperature.
EXISTENCE OF HAMILTONIAN κ-FACTOR
CAI Maocheng; FANG Qizhi; LI Yanjun
2004-01-01
A Hamiltonian k-factor is a k-factor containing a Hamiltonian cycle. An n/2-critical graph G is a simple graph of order n which satisfies δ(G) ≥ n/2 and δ(G - e) ＜ n/2for any edge e ∈ E(G). Let κ≥ 2 be an integer and G be an n/2-critical graph of even order n ≥ 8κ - 14. It is shown in this paper that for any given Hamiltonian cycle Cexcept that G - C consists of two components of odd orders when κ is odd, G has a k-factor containing C.
Orthogonal separable Hamiltonian systems on T2
无
2007-01-01
In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T2 for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T2 can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way.
On a general Heisenberg exchange effective Hamiltonian
Blanco, J.A.; Prida Pidal, V.M. [Dept. de Fisica, Oviedo Univ. (Spain)
1995-07-01
A general Heisenberg exchange effective Hamiltonian is deduced in a straightforward way from the elemental quantum mechanical principles for the case of magnetic ions with non-orbital degeneracy in a crystalline lattice. Expressions for the high order direct exchange coupling constants or parameters are presented. The meaning of this effective Hamiltonian is important because extracting information from the Heisenberg Hamiltonian is a difficult task and is however taken as the starting point for many quite profound investigations of magnetism in solids and therefore could play an important role in an introductory course to solid state physics. (author)
Algebraic Hamiltonian for Vibrational Spectra of Stibine
HOU Xi-Wen
2004-01-01
@@ An algebraic Hamiltonian, which in a limit can be reduced to an extended local mode model by Law and Duncan,is proposed to describe both stretching and bending vibrational energy levels of polyatomic molecules, where Fermi resonances between the stretches and the bends are considered. The Hamiltonian is used to study the vibrational spectra of stibine (SbH3). A comparison with the extended local mode model is made. Results of fitting the experimental data show that the algebraic Hamiltonian reproduces the observed values better than the extended local mode model.
Indirect quantum tomography of quadratic Hamiltonians
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Dicycle Cover of Hamiltonian Oriented Graphs
Khalid A. Alsatami
2016-01-01
Full Text Available A dicycle cover of a digraph D is a family F of dicycles of D such that each arc of D lies in at least one dicycle in F. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented graphs, Hamiltonian oriented complete bipartite graphs, and families of possibly non-Hamiltonian digraphs obtained from these digraphs via a sequence of 2-sum operations.
Improved Sufficient Conditions for Hamiltonian Properties
Bode Jens-P.
2015-05-01
Full Text Available In 1980 Bondy [2] proved that a (k+s-connected graph of order n ≥ 3 is traceable (s = −1 or Hamiltonian (s = 0 or Hamiltonian-connected (s = 1 if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1(n+s−1+1/2. It is shown in [1] that one can allow exceptional (k+ 1-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Hopf and homoclinic bifurcations for near-Hamiltonian systems
Tian, Yun; Han, Maoan
2017-02-01
We study homoclinic bifurcation of limit cycles in perturbed planar Hamiltonian systems. Suppose that a homoclinic loop is defined by H =hs. Our main result is that a new method is established for computing the coefficients of the expansion of Melnikov functions at h =hs. Then by using those coefficients, more limit cycles would be found around homoclinic loops. An example is also provided to illustrate our method.
Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions
Parry, A. O.; Swain, P S
1997-01-01
We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \\ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau mod...
Modification of logarithmic Hamiltonians and application of explicit symplectic-like integrators
Li, Dan; Wu, Xin
2017-08-01
We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or function) to both the kinetic energy and the force function. Explicit symplectic algorithms are available when the logarithmic Hamiltonian has two separable parts of coordinates and momenta. However, they are not if the logarithmic Hamiltonian is inseparable. Fortunately, they are still efficient by manipulating the logarithmic Hamiltonian as a new separable Hamiltonian in an extended phase space. In fact, they belong to symplectic-like integrators. The choice of mixing maps affects the performance of the considered symplectic-like integrators. It is shown that two maps about sequent permutations of coordinates and momenta are inferior to a map with mid-point permutations in some cases. The choice of the constant (or function) added also exerts some influence on the performance of the algorithms. As a result, with the help of the mid-point permutations and a suitable choice for the constant (or function) included, the logarithmic Hamiltonian methods bring an increase in accuracy compared to the non-logarithmic ones, particularly for highly eccentric orbits.
Effective stability for generalized Hamiltonian systems
CONG; Fuzhong; LI; Yong
2004-01-01
An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems,dimensions of action variables and angle variables might be distinct.
Spinor-Like Hamiltonian for Maxwellian Optics
Kulyabov D.S.
2016-01-01
Conclusions. For Maxwell equations in the Dirac-like form we can expand research methods by means of quantum field theory. In this form, the connection between the Hamiltonians of geometric, beam and Maxwellian optics is clearly visible.
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
Compressed quantum metrology for the Ising Hamiltonian
Boyajian, W. L.; Skotiniotis, M.; Dür, W.; Kraus, B.
2016-12-01
We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian that exhibits a quantum phase transition can be efficiently simulated on an exponentially smaller quantum computer. Specifically, by exploiting the fact that the ground state of such a Hamiltonian changes drastically around its phase-transition point, we construct a suitable observable from which one can estimate the relevant parameters of the Hamiltonian with Heisenberg scaling precision. We then show how, for the one-dimensional Ising Hamiltonian with transverse magnetic field acting on N spins, such a metrology protocol can be efficiently simulated on an exponentially smaller quantum computer while maintaining the same Heisenberg scaling for the squared error, i.e., O (N-2) precision, and derive the explicit circuit that accomplishes the simulation.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
Jacobi fields of completely integrable Hamiltonian systems
Giachetta, G.; Mangiarotti, L.; Sardanashvily, G
2003-03-31
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom make up an extended completely integrable system of 2m degrees of freedom, where m additional first integrals characterize a relative motion.
Polysymplectic Hamiltonian formalism and some quantum outcomes
Giachetta, G; Sardanashvily, G
2004-01-01
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Hamiltonian cycle problem and Markov chains
Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T
2014-01-01
This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Hamiltonian formulation of guiding center motion
Stern, D. P.
1971-01-01
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
Continuous finite element methods for Hamiltonian systems
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
On Hamiltonians Generating Optimal-Speed Evolutions
2008-01-01
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality ...
Hamiltonian Quantum Cellular Automata in 1D
Nagaj, Daniel; Wocjan, Pawel
2008-01-01
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process. We only require the ability to prepare an initial computational basis state which encodes both the quantum circuit and its input. The computational process is then carried out by the autonomous Hamiltonian time evolution. After a time polynomially long in th...
The matrix Hamiltonian for hadrons and the role of negative-energy components
Simonov, Yu. A.
2004-01-01
The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended ...
Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems
Liu, Chungen
2009-01-01
In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\\in C^2(\\Bbb R^{2n}, \\Bbb R)$ is super-quadratic and convex, for every number $\\tau>0$, there exists at least one $\\tau$-periodic brake orbit $(\\tau,x)$ with minimal period $\\tau$ or $\\tau/2$ provided $H(Nx)=H(x)$.
ANALYSIS OF LIMIT CYCLES TO A PERTURBED INTEGRABLE NON-HAMILTONIAN SYSTEM
无
2012-01-01
Bifurcation of limit cycles to a perturbed integrable non-Hamiltonian system is investigated using both qualitative analysis and numerical exploration.The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian system.The study reveals that the system has 3 limit cycles.By the method of numerical simulation,the distributed orderliness of the 3 limitcycles is observed,and their nicety places are determined.The study also indicates that each ...
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Hamiltonian Dynamics at Spatial Infinity.
Alexander, Matthew
We employ a projective construction of spatial infinity in four-dimensional spacetimes which are asymptotically flat. In this construction, points of the spatial boundary of the spacetime manifold are identified with congruences of asymptotically parallel spacelike curves that are asymptotically geodesic. It is shown that for this type of construction spatial infinity is represented by a three-dimensional timelike hyperboloid, and that this follows as a consequence of the vacuum Einstein equations. We then construct tensor fields which are defined at spatial infinity, and which embody the information carried by the gravitational field regarding the total mass, linear, and angular momentum of the spacetime. It is shown that these tensor fields must satisfy a set of second order partial differential field equations at spatial infinity. The asymptotic symmetry group implied by the projective construction is examined, and is identified with the Spi group. The field equations satisfied by the tensor fields at spatial infinity can be derived from an action principle, however this action does not appear to be related in any obvious way to the Hilbert-Einstein action of general relativity. Under mappings generated by the Spi group our Lagrangian is left form -invariant, and the corresponding Noether-conserved quantities are examined. It is found that for spacetimes which are stationary or axisymmetric, these conserved quantities are not the limits of the conserved quantities associated with the infinitesimal four-dimensional coordinate transformations. It is shown that using the tensor fields at spatial infinity one can define a set of canonical variables. Further, we show that the "time" derivatives of the configuration variables can be expressed in terms of some of the momentum densities; the remaining momentum densities are constrained. Finally, we construct the Hamiltonian, and examine the transformations generated by it.
Optical waveguide Hamiltonians leading to step-2 difference equations
Rueda-Paz, Juvenal; Wolf, Kurt Bernardo, E-mail: bwolf@fis.unam.mx [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Av. Universidad s/n, Cuernavaca, Morelos 62251 (Mexico)
2011-03-01
We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
On the Hamiltonian formalism of the tetrad-gravity
Lagraa, Meriem Hadjer; Touhami, Nabila
2016-01-01
We present a detailed analysis of the Hamiltonian constraints of the d-dimensional tetrad-gravity where the non-dynamical part of the spatial connection is fixed to zero. This new action depending on the co-tetrad and the dynamical part of the spatial connection leads to Lorentz, scalar and vectorial first-class polynomial constraints obeying a closed algebra in terms of Poisson brackets. This algebra closes on the structure constants instead of structure functions resulting from the Hamiltonian formalisms based on the A.D.M. decomposition. The same algebra of the reduced first-class constraints defined on the reduced phase-space, where the second-class constraints are solved, is obtained in terms of Dirac brackets. PACS numbers: 04.20.Cv, 04.20.Fy, 11.10.Ef, 11.30.Cp
Effective Hamiltonian and unitarity of the S matrix.
Rotter, I
2003-07-01
The properties of open quantum systems are described well by an effective Hamiltonian H that consists of two parts: the Hamiltonian H of the closed system with discrete eigenstates and the coupling matrix W between discrete states and continuum. The eigenvalues of H determine the poles of the S matrix. The coupling matrix elements W(cc')(k) between the eigenstates k of H and the continuum may be very different from the coupling matrix elements W(cc')(k) between the eigenstates of H and the continuum. Due to the unitarity of the S matrix, the W(cc')(k) depend on energy in a nontrivial manner. This conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighborhood of, respectively, avoided level crossings in the complex plane and double poles of the S matrix are given.
High-order Hamiltonian splitting for Vlasov-Poisson equations
Casas, Fernando; Faou, Erwan; Mehrenberger, Michel
2015-01-01
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions, we study the order conditions of such methods. It appears that these conditions are of Runge-Kutta-Nystr{\\"o}m type. In the one dimensional case, the order conditions can be further simplified, and efficient methods of order 6 with a reduced number of stages can be constructed. In the general case, high-order methods can also be constructed using explicit computations of commutators. Numerical results are performed and show the benefit of using high-order splitting schemes in that context. Complete and self-contained proofs of convergence results and rigorous error estimates are also given.
Optical waveguide Hamiltonians leading to step-2 difference equations
Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2011-03-01
We examine the evolution of an N-point signal produced and sensed at finite arrays of points transverse to a planar waveguide, within the framework of the finite quantization of geometric optics. In contradistinction to the common mechanical Hamiltonians (kinetic plus potential energy terms) the classical waveguide Hamiltonian is the square root of a difference of squares of the refractive index profile minus the optical momentum. The finitely quantized model requires the solution of the square eigenvalue and eigenfunction problem which leads to a step-two difference equation that contains two solutions and two signs of energy. We find the proper linear combinations to fit the Kravchuk functions of the finite oscillator model.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Modular Hamiltonian of Excited States in Conformal Field Theory
Lashkari, Nima
2015-01-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the replica Z_n symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Solving a Hamiltonian Path Problem with a bacterial computer
Treece Jessica
2009-07-01
Full Text Available Abstract Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node
Hamiltonian formalism for Perturbed Black Hole Spacetimes
Mihaylov, Deyan; Gair, Jonathan
2017-01-01
Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C. P.; Baza, S
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is als...
Law, Sean M; Ahlstrom, Logan S; Panahi, Afra; Brooks, Charles L
2014-10-02
Molecular recognition by intrinsically disordered proteins (IDPs) plays a central role in many critical cellular processes. Toward achieving detailed mechanistic understanding of IDP-target interactions, here we employ the "Hamiltonian mapping" methodology, which is rooted in the weighted histogram analysis method (WHAM), for the fast and efficient calibration of structure-based models in studies of IDPs. By performing reference simulations on a given Hamiltonian, we illustrate for two model IDPs how this method can extrapolate thermodynamic behavior under a range of modified Hamiltonians, in this case representing changes in the binding affinity (Kd) of the system. Given sufficient conformational sampling in a single trajectory, Hamiltonian mapping accurately reproduces Kd values from direct simulation. This method may be generally applied to systems beyond IDPs in force field optimization and in describing changes in thermodynamic behavior as a function of external conditions for connection with experiment.
Shestakova, T P
2013-01-01
We construct Hamiltonian dynamics of the generalized spherically symmetric gravitational model in extended phase space. We start from the Faddeev - Popov effective action with gauge-fixing and ghost terms, making use of gauge conditions in differential form. It enables us to introduce missing velocities into the Lagrangian and then construct a Hamiltonian function according a usual rule which is applied for systems without constraints. The main feature of Hamiltonian dynamics in extended phase space is that it can be proved to be completely equivalent to Lagrangian dynamics derived from the effective action. The sets of Lagrangian and Hamiltonian equations are not gauge invariant in general. We demonstrate that solutions to the obtained equations include those of the gauge invariant Einstein equations, and also discuss a possible role of gauge-noninvariant terms. Then, we find a BRST invariant form of the effective action by adding terms not affecting Lagrangian equations. After all, we construct the BRST cha...
Ajoy, Ashok; Cappellaro, Paola
2013-05-31
We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Li, Jun-Qing; Miao, Yan-Gang; Xue, Zhao
2014-01-01
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Jun-Qing Li
Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.
Multidimensional Hamiltonian for tunneling with position-dependent mass.
Fernández-Ramos, Antonio; Smedarchina, Zorka; Siebrand, Willem
2014-09-01
A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.
On the quantum mechanics of bicomplex Hamiltonian system
Banerjee, Abhijit
2017-02-01
We investigate the Schrödinger equation in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. We propose an analytical method to solve bicomplex-version of Schrödinger equation corresponding to the systems of Hamiltonians of both hermitian (self-adjoint) and non-hermitian PT symmetric type. In our approach we extend the existing mathematical formulation of quantum system searching for the exact or quasi-exact solution for ground state energy eigenvalues and associated wave functions acting in bicomplex Hilbert space. The model concerning hermitian Hamiltonians is then applied to the problems of two bicomplex valued polynomial oscillators one involving x2 and another of isotonic type. The ground states and associated energy values for both the oscillators are found to be hyperbolic in nature. The model in connection to the unbroken PT symmetric Hamiltonians is then applied to illustrate the problems of complex and bicomplex valued shifted oscillators.
Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
Sheftel, Mikhail; Yazıcı, Devrim
2016-09-01
We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator J_0 we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on J_0, we generate another two Hamiltonian operators J_+ and J_- and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of J_0, J_+ and J_- with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.
Gravitational surface Hamiltonian and entropy quantization
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Gravitational surface Hamiltonian and entropy quantization
Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-02-01
The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
Manifest Covariant Hamiltonian Theory of General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating a manifest covariant Hamiltonian theory of General Relativity in the presence of source fields is addressed, by extending the so-called "DeDonder-Weyl" formalism to the treatment of classical fields in curved space-time. The theory is based on a synchronous variational principle for the Einstein equation, formulated in terms of superabundant variables. The technique permits one to determine the continuum covariant Hamiltonian structure associated with the Einstein equation. The corresponding continuum Poisson bracket representation is also determined. The theory relies on first-principles, in the sense that the conclusions are reached in the framework of a non-perturbative covariant approach, which allows one to preserve both the 4-scalar nature of Lagrangian and Hamiltonian densities as well as the gauge invariance property of the theory.
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Effective Hamiltonians for phosphorene and silicene
Voon, L. C. Lew Yan; Lopez-Bezanilla, A.; Wang, J.;
2015-01-01
We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field andmagnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (NewJ. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene.......Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expressionfor band warping is obtained analytically and found to be of different order than for graphene. Weprove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature...
Hamiltonian Dynamics of Protein Filament Formation.
Michaels, Thomas C T; Cohen, Samuel I A; Vendruscolo, Michele; Dobson, Christopher M; Knowles, Tuomas P J
2016-01-22
We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
Hamiltonian dynamics for complex food webs.
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Hamiltonian adaptive resolution simulation for molecular liquids.
Potestio, Raffaello; Fritsch, Sebastian; Español, Pep; Delgado-Buscalioni, Rafael; Kremer, Kurt; Everaers, Ralf; Donadio, Davide
2013-03-08
Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.
Stability of Frustration-Free Hamiltonians
Michalakis, Spyridon
2011-01-01
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al., on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Hamiltonian theory of guiding-center motion
Cary, John R.; Brizard, Alain J. [Center for Integrated Plasma Studies and Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States) and Tech-X Corporation, Boulder, Colorado 80303 (United States); Department of Chemistry and Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States)
2009-04-15
Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether's theorem (hence invariants follow from symmetries), and they preserve the Poincare invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields--something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time
Hamiltonian dynamics of the parametrized electromagnetic field
G., J Fernando Barbero; Villaseñor, Eduardo J S
2015-01-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Hamiltonian dynamics of the parametrized electromagnetic field
Barbero G, J. Fernando; Margalef-Bentabol, Juan; Villaseñor, Eduardo J. S.
2016-06-01
We study the Hamiltonian formulation for a parametrized electromagnetic field with the purpose of clarifying the interplay between parametrization and gauge symmetries. We use a geometric approach which is tailor-made for theories where embeddings are part of the dynamical variables. Our point of view is global and coordinate free. The most important result of the paper is the identification of sectors in the primary constraint submanifold in the phase space of the model where the number of independent components of the Hamiltonian vector fields that define the dynamics changes. This explains the non-trivial behavior of the system and some of its pathologies.
Convergence to equilibrium under a random Hamiltonian.
Brandão, Fernando G S L; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Incorporation of New Information in an Approximate Hamiltonian
Viazminsky, C P
2002-01-01
Additional information about the eigenvalues and eigenvectors of a physical system demands extension of the effective Hamiltonian in use. In this work we extend the effective Hamiltonian that describes partially a physical system so that the new Hamiltonian comprises, in addition to the information in the old Hamiltonian, new information, available by means of experiment or theory. A simple expression of the enlarged Hamiltonian, which does not involve matrix inversion, is obtained. It is also shown that the Lee-Suzuki transformation effectively put the initial Hamiltonian in a diagonal block form.
The Hamiltonian formulation of general relativity: myths and reality
Kiriushcheva, Natalia; Kuzmin, Sergei
2011-06-01
Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric g μν to lapse and shift functions and the three-metric g km, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.
Szalay, Viktor
2015-05-07
A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.
An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian
Dyall, Kenneth G.
1994-01-01
The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
Ultimate generalization of Noether's theorem in the realm of Hamiltonian point dynamics
Struckmeier, Jürgen
2012-01-01
Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually derived in the Lagrangian formalism, the natural context for deriving Noether's theorem for first-order Lagrangian systems is the Hamiltonian formalism. The reason is that the class of transformations that leave the action functional invariant coincides with the class of canonical transformations. As a result, any invariant of a Hamiltonian system can be correlated with a symmetry transformation simply by means of the canonical transformation rules. As this holds for any invariant, we thereby obtain the most general representation of Noether's theorem. In order to allow for symmetry mappings that include a transformation of time, we must refer to the extended Hamiltonian formalism. This formalism enables us to define generating functions of canonical transformations that al...
Implicit Hamiltonian formulation of bond graphs
Golo, G.; Schaft, A.J. van der; Breedveld, P.C.; Maschke, B.M.
2003-01-01
This paper deals with mathematical formulation of bond graphs. It is proven that the power continuous part of bond graphs, the junction structure, can be associated with a Dirac structure and that equations describing a bond graph model correspond to an implicit port-controlled Hamiltonian system wi
Hamiltonian Approach to the Gribov Problem
Heinzl, T
1996-01-01
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
Edge-disjoint Hamiltonian cycles in hypertournaments
Thomassen, Carsten
2006-01-01
We introduce a method for reducing k-tournament problems, for k >= 3, to ordinary tournaments, that is, 2-tournaments. It is applied to show that a k-tournament on n >= k + 1 + 24d vertices (when k >= 4) or on n >= 30d + 2 vertices (when k = 3) has d edge-disjoint Hamiltonian cycles if and only...
Linear Hamiltonian Behaviors and Bilinear Differential Forms
Rapisarda, P.; Trentelman, H.L.
2004-01-01
We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows us to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences and allows us to study
Discrete variable representation for singular Hamiltonians
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...
Bifurcations and safe regions in open Hamiltonians
Barrio, R; Serrano, S [GME, Dpto Matematica Aplicada and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Blesa, F [GME, Dpto Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es, E-mail: fblesa@unizar.es, E-mail: sserrano@unizar.es
2009-05-15
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Henon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Bifurcations and safe regions in open Hamiltonians
Barrio, R.; Blesa, F.; Serrano, S.
2009-05-01
By using different recent state-of-the-art numerical techniques, such as the OFLI2 chaos indicator and a systematic search of symmetric periodic orbits, we get an insight into the dynamics of open Hamiltonians. We have found that this kind of system has safe bounded regular regions inside the escape region that have significant size and that can be located with precision. Therefore, it is possible to find regions of nonzero measure with stable periodic or quasi-periodic orbits far from the last KAM tori and far from the escape energy. This finding has been possible after a careful combination of a precise 'skeleton' of periodic orbits and a 2D plate of the OFLI2 chaos indicator to locate saddle-node bifurcations and the regular regions near them. Besides, these two techniques permit one to classify the different kinds of orbits that appear in Hamiltonian systems with escapes and provide information about the bifurcations of the families of periodic orbits, obtaining special cases of bifurcations for the different symmetries of the systems. Moreover, the skeleton of periodic orbits also gives the organizing set of the escape basin's geometry. As a paradigmatic example, we study in detail the Hénon-Heiles Hamiltonian, and more briefly the Barbanis potential and a galactic Hamiltonian.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
Hamiltonian analysis of BHT massive gravity
Blagojević, M
2010-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants $(\\Lambda_0,m^2)$, our canonical analysis reveals the special role of the condition $\\Lambda_0/m^2\
Hamiltonian and self-adjoint control systems
Schaft, A. van der; Crouch, P.E.
1987-01-01
This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian realization. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoin
Hamiltonian constants for several new entire solutions
2008-01-01
Using the Hamiltonian identities and the corresponding Hamilto- nian constants for entire solutions of elliptic partial differential equations, we investigate several new entire solutions whose existence were shown recently, and show interesting properties of the solutions such as formulas for contact angles at infinity of concentration curves.
Transparency in Port-Hamiltonian-Based Telemanipulation
Secchi, Cristian; Stramigioli, Stefano; Fantuzzi, Cesare
2008-01-01
After stability, transparency is the major issue in the design of a telemanipulation system. In this paper, we exploit the behavioral approach in order to provide an index for the evaluation of transparency in port-Hamiltonian-based teleoperators. Furthermore, we provide a transparency analysis of p
Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation
Mane, S R
2016-01-01
A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.
Notch filters for port-Hamiltonian systems
Dirksz, Daniel; Scherpen, Jacquelien M.A.; van der Schaft, Abraham; Steinbuch, M.
2012-01-01
Network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, i.e., port-Hamiltonian (PH) systems [4, 6]. The PH modeling framework describes a large class of (nonlinear) systems including passive mechanical systems, electrical systems, electromec
The Maslov indices of Hamiltonian periodic orbits
Gosson, Maurice de [Blekinge Institute of Technology, SE 371 79 Karlskrona (Sweden); Gosson, Serge de [Vaexjoe University (MSI), SE 351 95 Vaexjoe (Sweden)
2003-12-05
We use the properties of the Leray index to give precise formulae in arbitrary dimensions for the Maslov index of the monodromy matrix arising in periodic Hamiltonian systems. We compare our index with other indices appearing in the literature. (letter to the editor)
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our
Global Properties of Integrable Hamiltonian Systems
Lukina, O.V.; Takens, F.; Broer, H.W.
2008-01-01
This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approa
Scattering for Infinite Dimensional Port Hamiltonian Systems
Macchelli, Alessandro; Stramigioli, Stefano; Schaft, Arjan van der; Melchiorri, Claudio
2002-01-01
In this paper, an introduction to scattering for infinite dimensional systems within the framework of port Hamiltonian system is presented. The classical results on wave propagation can be extended to generic power propagation phenomena, for example to fluid dynamics or flexible structures. The key-
Scattering matrix of arbitrary tight-binding Hamiltonians
Ramírez, C.; Medina-Amayo, L. A.
2017-03-01
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.
Hamiltonian YM 2+1: note on point splitting regularization
Schulz, Hermann
2016-01-01
The Hamiltonian of 2+1 dimensional Yang Mills theory was derived by Karabali, Kim and Nair by using point splitting regularization. But in calculating e.g. the vacuum wave functional this scheme was left in favour of arguments. Here we follow up a conjecture of Leigh, Minic and Yelnikov of how this gap might be filled by including all positive powers of the regularization parameter ($\\ep \\to +0$). Admittedly, though we concentrate on the ground state in the large $N$ limit, only two such powers could be included due to the increasing complexity of the task.
Effective Hamiltonian approach to periodically perturbed quantum optical systems
Sainz, I. [Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon, 47460 Lagos de Moreno, Jal. (Mexico)]. E-mail: isa@culagos.udg.mx; Klimov, A.B. [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410 Guadalajara, Jal. (Mexico)]. E-mail: klimov@cencar.udg.mx; Saavedra, C. [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: csaaved@udec.cl
2006-02-20
We apply the method of Lie-type transformations to Floquet Hamiltonians for periodically perturbed quantum systems. Some typical examples of driven quantum systems are considered in the framework of this approach and corresponding effective time dependent Hamiltonians are found.
Integrable Coupling of KN Hierarchy and Its Hamiltonian Structure
GUO Fu-Kui; ZHANG Yu-Feng
2006-01-01
The Hamiltonian structure of the integrable couplings obtained by our method has not been solved. In this paper, the Hamiltonian structure of the KN hierarchy is obtained by making use of the quadratic-form identity.
Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy
Brunelli, J. C.
1996-01-01
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two ones the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system.
Nonconventional fluctuation dissipation process in non-Hamiltonian dynamical systems
Bianucci, Marco
2016-08-01
Here, we introduce a statistical approach derived from dynamics, for the study of the geophysical fluid dynamics phenomena characterized by a weak interaction among the variables of interest and the rest of the system. The approach is reminiscent of the one developed some years ago [M. Bianucci, R. Mannella, P. Grigolini and B. J. West, Phys. Rev. E 51, 3002 (1995)] to derive statistical mechanics of macroscopic variables on interest starting from Hamiltonian microscopic dynamics. However, in the present work, we are interested to generalize this approach beyond the context of the foundation of thermodynamics, in fact, we take into account the cases where the system of interest could be non-Hamiltonian (dissipative) and also the interaction with the irrelevant part can be of a more general type than Hamiltonian. As such example, we will refer to a typical case from geophysical fluid dynamics: the complex ocean-atmosphere interaction that gives rise to the El Niño Southern Oscillation (ENSO). Here, changing all the scales, the role of the “microscopic” system is played by the atmosphere, while the ocean (or some ocean variables) plays the role of the intrinsically dissipative macroscopic system of interest. Thus, the chaotic and divergent features of the fast atmosphere dynamics remains in the decaying properties of the correlation functions and of the response function of the atmosphere variables, while the exponential separation of the perturbed (or close) single trajectories does not play a direct role. In the present paper, we face this problem in the frame of a not formal Langevin approach, limiting our discussion to physically based rather than mathematics arguments. Elsewhere, we obtain these results via a much more formal procedure, using the Zwanzing projection method and some elements from the Lie Algebra field.
A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
2014-09-01
We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.
A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism
Batalin, Igor A; Tyutin, Igor V
2014-01-01
We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Batalin, Igor A; Tyutin, Igor V
2014-01-01
We study systematically finite BRST-BFV transformations in $Sp(2)$-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.
2014-09-01
We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
Deformations of the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity.
Krasnov, Kirill
2008-02-29
We show that the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity can be nontrivially deformed by allowing the cosmological constant to become an arbitrary function of the (Weyl) curvature. Our result implies that there is not one but infinitely many (parametrized by an arbitrary function) four-dimensional generally covariant local gravity theories propagating 2 degrees of freedom.
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
HAMILTONIAN MECHANICS ON K(A)HLER MANIFOLDS
无
2006-01-01
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.
Introduction to thermodynamics of spin models in the Hamiltonian limit
Berche, B; Berche, Bertrand; Lopez, Alexander
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.
Landau hamiltonians with random potentials localization and the density of states
Combes, J M; Combes, J M; Hislop, P D
1994-01-01
We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finite-area Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.
Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type
Tsuda, Teruhisa
2010-01-01
In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems. The main purpose of this paper is to present particular solutions of this Hamlitonian system in terms of a certain generalization of Gauss' hypergeometric function. Key ingredients of the argument are the linear Pfaffian system derived from an integral representation of the hypergeometric function (with the aid of twisted de Rham theory) and Lax formalism of the Hamiltonian system.
Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables
Giachetta, G; Sardanashvily, G
2002-01-01
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus. These variables enable one to choose the angle polarization which otherwise is not easily determined. It is spanned by almost-Hamiltonian vector fields of angle variables. The associated quantum algebra consists of functions affine in action coordinates. We show that this algebra has a continuum set of nonequivalent representations in the separable pre-Hilbert space of smooth complex functions on the torus. The spectrum of the action operators is obtained.
Hamiltonian[k,k+1]-因子%Hamiltonian [k, k + 1]-Factor
蔡茂诚; 方奇志; 李延军
2003-01-01
A Hamiltonian [k, k + 1]-factor is a [k, k + 1]-factor containing a Hamiltonian cycle. A simple graph G of order n is n/2-critical if δ(G) ≥ n/2 but δ(G - e) ＜ n/2 for any edge e ∈ E(G). Let k ≥ 2 be an integer and G be an n/2-critical graph with n ≥ 4k - 6 and n ≥ 7. In this paper it is proved that for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. This result is an improvement on some recent results about the existence of Hamiltonian [k, k + 1]-factor.%本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性.Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\\e)＜n/2(对任意的e∈E(G)),则称G为n/2-临界图.设k为大于等于2的整数,G为n/2-临界图(其中n≥4k-6且n≥7),我们证明了对于G的任何Hamiltonian圈C,G中必存在包含C的[k,k+1]-因子.该结果改进了现有的一些有关Hamiltonian[k,k+1]-因子存在性的结果.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K
2009-01-01
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and develops the approach of I.Krichever treating the $\\gl(n)$ case. For every Lax operator considered as the mapping sending a point of the cotangent bundle on the space of extended Tyrin data to an element of the corresponding Lax operator algebra we construct the hierarchy of mutually commuting flows given by Lax equations and prove that those are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example we derive elliptic $A_n$, $C_n$, $D_n$ Calogero-Moser systems in frame of our approach.
Lax operator algebras and Hamiltonian integrable hierarchies
Sheinman, Oleg K [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-02-28
This paper considers the theory of Lax equations with a spectral parameter on a Riemann surface, proposed by Krichever in 2001. The approach here is based on new objects, the Lax operator algebras, taking into consideration an arbitrary complex simple or reductive classical Lie algebra. For every Lax operator, regarded as a map sending a point of the cotangent bundle on the space of extended Tyurin data to an element of the corresponding Lax operator algebra, a hierarchy of mutually commuting flows given by the Lax equations is constructed, and it is proved that they are Hamiltonian with respect to the Krichever-Phong symplectic structure. The corresponding Hamiltonians give integrable finite-dimensional Hitchin-type systems. For example, elliptic A{sub n}, C{sub n}, and D{sub n} Calogero-Moser systems are derived in the framework of our approach. Bibliography: 13 titles.
Hamiltonian Approach To Dp-Brane Noncommutativity
Nikolic, B.; Sazdovic, B.
2010-07-01
In this article we investigate Dp-brane noncommutativity using Hamiltonian approach. We consider separately open bosonic string and type IIB superstring which endpoints are attached to the Dp-brane. From requirement that Hamiltonian, as the time translation generator, has well defined derivatives in the coordinates and momenta, we obtain boundary conditions directly in the canonical form. Boundary conditions are treated as canonical constraints. Solving them we obtain initial coordinates in terms of the effective ones as well as effective momenta. Presence of momenta implies noncommutativity of the initial coordinates. Effective theory, defined as initial one on the solution of boundary conditions, is its Ω even projection, where Ω is world-sheet parity transformation Ω:σ→-σ. The effective background fields are expressed in terms of Ω even and squares of the Ω odd initial background fields.
ON THE ELUSIVENESS OF HAMILTONIAN PROPERTY
高随祥
2001-01-01
Decision tree complexity is an important measure of computational complexity. A graph property is a set of graphs such that if some graph G is in the set then each isomorphic graph to G is also in the set. Let P be a graph property on n vertices, if every decision tree algorithm recognizing P must examine at least k pairs of vertices in the worst case, then it is said that the decision tree complexity of P is k. If every decision tree algorithm recognizing P must examine all n(n-1)/2 pairs of vertices in the worst case, then P is said to be elusive. Karp conjectured that every nontrivial monotone graph property is elusive. This paper concerns the elusiveness of Hamiltonian property. It is proved that if n=p+1, pq or pq+1, (where p,q are distinct primes),then Hamiltonian property on n vertices is elusive.
A Hamiltonian Formulation of Topological Gravity
Waelbroeck, Henri
2009-01-01
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.
Quantum Hamiltonian complexity and the detectability lemma
Aharonov, Dorit; Landau, Zeph; Vazirani, Umesh
2010-01-01
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint satisfaction (such as SAT), with the additional ingredient of multi-particle entanglement. This additional ingredient of course makes generalizations of celebrated theorems such as the PCP theorem from classical to the quantum domain highly non-trivial; it also raises entirely new questions such as bounds on entanglement and correlations in ground states, and in particular area laws. We propose a simple combinatorial tool that helps to handle such questions: it is a simplified, yet more general version of the detectability lemma introduced by us in the more restricted context on quantum gap amplification a year ago. Here, we argue that this lemma is applicable in much more general contexts. We use it to provide a simplified and more combinatorial proof of Hastings' 1D area law...
General formalism for singly thermostated Hamiltonian dynamics.
Ramshaw, John D
2015-11-01
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.
Hamiltonian partial differential equations and applications
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Hamiltonian hierarchy and the Hulthen potential
Gönül, B
2000-01-01
We deal with the Hamiltonian hierarchy problem of the Hulth\\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal barrier. Incorporating the supersymmetric solutions and using the first-order perturbation theory we obtain an expression for the energy levels of theHulth\\'{e}n potential which gives satisfactory values for the non-zero angular momentum states.
Hamiltonian theory of guiding-center motion
Littlejohn, R.G.
1980-05-01
A Hamiltonian treatment of the guiding center problem is given which employs noncanonical coordinates in phase space. Separation of the unperturbed system from the perturbation is achieved by using a coordinate transformation suggested by a theorem of Darboux. As a model to illustrate the method, motion in the magnetic field B=B(x,y)z is studied. Lie transforms are used to carry out the perturbation expansion.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
Information, disturbance and Hamiltonian quantum feedback control
Doherty, A C; Jungman, G; Doherty, Andrew C.; Jacobs, Kurt; Jungman, Gerard
2001-01-01
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the minimal constraint that the available strength of both is limited. This motivates concepts of information extraction and disturbance which are distinct from those usually considered in quantum information theory. Using these concepts we identify an information trade-off in quantum feedback control.
Obtaining breathers in nonlinear Hamiltonian lattices
Flach, S
1995-01-01
Abstract We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.
Monte Carlo Hamiltonian:Inverse Potential
LUO Xiang-Qian; CHENG Xiao-Ni; Helmut KR(O)GER
2004-01-01
The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system,using Monte Carlo(MC)algorithm with importance sampling.However,conventional MC algorithm has some difficulties when applied to inverse potentials.We propose to use effective potential and extrapolation method to solve the problem.We present examples from the hydrogen system.
Spectral analysis of tridiagonal Fibonacci Hamiltonians
Yessen, William
2011-01-01
We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.
Gauge symmetry enhancement in Hamiltonian formalism
Hong, S T; Lee, T H; Oh, P; Oh, Phillial
2003-01-01
We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.
The Effective Hamiltonian in the Scalar Electrodynamics
Dineykhan, M D; Zhaugasheva, S A; Sakhyev, S K
2002-01-01
On the basis of an investigation of the asymptotic behaviour of the polarization loop for the scalar particles in the external electromagnetic field the relativistic corrections to the Hamiltonian are determined. The constituent mass of the particles in the bound state is analytically derived. It is shown that the constituent mass of the particles differs from the mass of the particles in the free state. The corrections connected with the Thomas precession have been calculated.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Optimal Hamiltonian Simulation by Quantum Signal Processing
Low, Guang Hao; Chuang, Isaac L.
2017-01-01
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a d -sparse Hamiltonian H ^ for time-interval t with error ɛ is O [t d ∥H ^ ∥max+log (1 /ɛ ) /log log (1 /ɛ ) ] , which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (i) transducing eigenvalues of H ^ into a single ancilla qubit, (ii) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (iii) projecting this ancilla with near unity success probability.
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, Makoto; Chua, Leon
In this paper, we show that any n-dimensional autonomous systems can be regarded as subsystems of 2n-dimensional Hamiltonian systems. One of the two subsystems is identical to the n-dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto n-dimensional spheres, or n-dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as n-dimensional autonomous systems.
Exploiting time-independent Hamiltonian structure as controls for manipulating quantum dynamics.
Beltrani, Vincent; Rabitz, Herschel
2012-09-07
The opportunities offered by utilizing time-independent Hamiltonian structure as controls are explored for manipulating quantum dynamics. Two scenarios are investigated using different manifestations of Hamiltonian structure to illustrate the generality of the concept. In scenario I, optimally shaped electrostatic potentials are generated to flexibly control electron scattering in a two-dimensional subsurface plane of a semiconductor. A simulation is performed showing the utility of optimally setting the individual voltages applied to a multi-pixel surface gate array in order to produce a spatially inhomogeneous potential within the subsurface scattering plane. The coherent constructive and destructive electron wave interferences are manipulated by optimally adjusting the potential shapes to alter the scattering patterns. In scenario II, molecular vibrational wave packets are controlled by means of optimally selecting the Hamiltonian structure in cooperation with an applied field. As an illustration of the concept, a collection (i.e., a level set) of dipole functions is identified where each member serves with the same applied electric field to produce the desired final transition probability. The level set algorithm additionally found Hamiltonian structure controls exhibiting desirable physical properties. The prospects of utilizing the applied field and Hamiltonian structure simultaneously as controls is also explored. The control scenarios I and II indicate the gains offered by algorithmically guided molecular or material discovery for manipulating quantum dynamics phenomenon.
Singh, Parampreet; Soni, S. K.
2016-06-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.
A Class of Hamiltonians for a Three-Particle Fermionic System at Unitarity
Correggi, M., E-mail: michele.correggi@gmail.com [Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Dipartimento di Matematica e Fisica (Italy); Dell’Antonio, G. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy); Finco, D. [Università Telematica Internazionale Uninettuno, Corso V. Emanuele II 39, Facoltà di Ingegneria (Italy); Michelangeli, A. [Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265 (Italy); Teta, A. [“Sapienza” Università di Roma, P.le A. Moro 5, Dipartimento di Matematica (Italy)
2015-12-15
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass m, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for m larger than a critical value m{sup ∗} ≃ (13.607){sup −1} a self-adjoint and lower bounded Hamiltonian H{sub 0} can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for m ∈ (m{sup ∗},m{sup ∗∗}), where m{sup ∗∗} ≃ (8.62){sup −1}, there is a further family of self-adjoint and lower bounded Hamiltonians H{sub 0,β}, β ∈ ℝ, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.
Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system
Restuccia Alvaro
2016-01-01
Full Text Available We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose field equations are the ε-parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ε → 0 the lagrangians reduce to the ones of the coupled KdV system while, after a suitable redefinition of the fields, in the strong limit ε → ∞ we obtain the lagrangians of the coupled modified KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ε → 0 and ε → ∞.
Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system
Restuccia, Alvaro; Sotomayor, Adrián
2016-01-01
We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose field equations are the ɛ-parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ɛ → 0 the lagrangians reduce to the ones of the coupled KdV system while, after a suitable redefinition of the fields, in the strong limit ɛ → ∞ we obtain the lagrangians of the coupled modified KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ɛ → 0 and ɛ → ∞.
Sachin Kumar; K Singh; R K Gupta
2012-07-01
In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (′/)-expansion methodc, where = () satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
Some sufficient conditions for Hamiltonian property in terms of Wiener-type invariants
Meijun Kuang; Guihua Huang; Hanyuan Deng
2016-02-01
The Wiener-type invariants of a simple connected graph = (,) can be expressed in terms of the quantities $W_{f} = \\sum_{\\{u,v\\}\\subseteq V} f (d_{G}(u, v))$ for various choices of the function (), where (, ) is the distance between vertices and in . In this paper, we give some sufficient conditions for a connected graph to be Hamiltonian, a connected graph to be traceable, and a connected bipartite graph to be Hamiltonian in terms of the Wiener-type invariants.
Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs
Andrey V. Sokolov
2011-12-01
Full Text Available This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.
Delshams, A; Seara, T M
2003-01-01
We consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian possessing an $n$-dimensional hyperbolic invariant torus with fast frequencies $\\omega/\\sqrt\\varepsilon$ and coincident whiskers, plus a perturbation of order $\\mu=\\varepsilon^p$. The vector $\\omega$ is assumed to satisfy a Diophantine condition. We provide a tool to study, in this singular case, the splitting of the perturbed whiskers for $\\varepsilon$ small enough, as well as their homoclinic intersections, using the Poincar\\'e--Melnikov method. Due to the exponential smallness of the Melnikov function, the size of the error term has to be carefully controlled. So we introduce flow-box coordinates in order to take advantage of the quasiperiodicity properties of the splitting. As a direct application of this approach, we obtain quite general upper bounds for the splitting.
Delshams, A
2003-01-01
We consider an example of singular or weakly hyperbolic Hamiltonian, with 3 degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian possessing a 2-dimensional hyperbolic invariant torus with fast frequencies $\\omega/\\sqrt\\varepsilon$ and coincident whiskers, plus a perturbation of order $\\mu=\\varepsilon^p$. We choose $\\omega$ as the golden vector. Our aim is to obtain asymptotic estimates for the splitting, proving the existence of transverse intersections between the perturbed whiskers for $\\varepsilon$ small enough, by applying the Poincar\\'e--Melnikov method together with a accurate control of the size of the error term. The good arithmetic properties of the golden vector allow us to prove that the splitting function has 4 simple zeros (corresponding to nondegenerate critical points of the splitting potential), giving rise to 4 transverse homoclinic orbits. More precisely, we show that a shift of these orbi...
Delshams, A
2003-01-01
We consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian possessing an $n$-dimensional hyperbolic invariant torus with fast frequencies $\\omega/\\sqrt\\varepsilon$ and coincident whiskers, plus a perturbation of order $\\mu=\\varepsilon^p$. The vector $\\omega$ is assumed to satisfy a Diophantine condition. We provide a tool to study, in this singular case, the splitting of the perturbed whiskers for $\\varepsilon$ small enough, as well as their homoclinic intersections, using the Poincar\\'e--Melnikov method. Due to the exponential smallness of the Melnikov function, the size of the error term has to be carefully controlled. So we introduce flow-box coordinates in order to take advantage of the quasiperiodicity properties of the splitting. As a direct application of this approach, we obtain quite general upper bounds for the splitting.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
Gosset, David; Terhal, Barbara M; Vershynina, Anna
2015-04-10
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
Rey, Michaël; Nikitin, Andrei V; Tyuterev, Vladimir G
2012-06-28
A rovibrational model based on the normal-mode complete nuclear Hamiltonian is applied to methane using our recent potential energy surface [A. V. Nikitin, M. Rey, and Vl. G. Tyuterev, Chem. Phys. Lett. 501, 179 (2011)]. The kinetic energy operator and the potential energy function are expanded in power series to which a new truncation-reduction technique is applied. The vibration-rotation Hamiltonian is transformed systematically to a full symmetrized form using irreducible tensor operators. Each term of the Hamiltonian expansion can be thus cast in the tensor form whatever the order of the development. This allows to take full advantage of the symmetry properties for doubly and triply degenerate vibrations and vibration-rotation states. We apply this model to variational computations of energy levels for (12)CH(4), (13)CH(4), and (12)CD(4).
Hamiltonian formulation of generalized quantum dynamics——Quantum mechanical problem
吴宁; 阮图南
1997-01-01
The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations.
Tidal wave in $^{102}$Pd: An extended five-dimensional collective Hamiltonian description
Wang, Y Y; Chen, Q B; Zhang, S Q; Song, C Y
2016-01-01
The five-dimensional collective Hamiltonian based on the covariant density functional theory is applied to investigate the observed tidal wave mode in the yrast band of $^{102}$Pd. The energy spectra, the relations between the spin and the rotational frequency, and the ratios of $B(E2)/\\mathcal{J}(I)$ in the yrast band are well reproduced by introducing the empirical $ab$ formula for the moments of inertia. This $ab$ formula is related to the fourth order effect of collective momentum in the collective Hamiltonian. It is also shown that the shape evolution in the tidal wave is determined microscopically by the competition between the rotational kinetic energy and the collective potential in the framework of the collective Hamiltonian.
Kinematics of fluid particles on the sea surface. Part 1. Hamiltonian theory
Fedele, Francesco; Farazmand, Mohammad
2015-01-01
We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and traveling waves we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.
Single-valued Hamiltonian via Legendre–Fenchel transformation and time translation symmetry
Chi, Huan-Hang, E-mail: hhchi@stanford.edu [Physics Department, Stanford University, Stanford, CA 94305 (United States); Institute of Modern Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084 (China); Physics Department, Tsinghua University, Beijing 100084 (China); He, Hong-Jian, E-mail: hjhe@tsinghua.edu.cn [Institute of Modern Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084 (China); Physics Department, Tsinghua University, Beijing 100084 (China); Center for High Energy Physics, Peking University, Beijing 100871 (China)
2014-08-15
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre–Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.
Renormalization Group Flows of Hamiltonians Using Tensor Networks
Bal, M.; Mariën, M.; Haegeman, J.; Verstraete, F.
2017-06-01
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015), 10.1103/PhysRevLett.115.180405; S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017), 10.1103/PhysRevLett.118.110504], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.
Hamiltonian formulation of surfaces with constant Gaussian curvature
Trejo, Miguel; Amar, Martine Ben; Mueller, Martin Michael [Laboratoire de Physique Statistique de l' Ecole Normale Superieure (UMR 8550), associe aux Universites Paris 6 et Paris 7 et au CNRS, 24, rue Lhomond, 75005 Paris (France)
2009-10-23
Dirac's method for constrained Hamiltonian systems is used to describe surfaces of constant Gaussian curvature. A geometrical free energy, for which these surfaces are equilibrium states, is introduced and interpreted as an action. An equilibrium surface can then be generated by the evolution of a closed space curve. Since the underlying action depends on second derivatives, the velocity of the curve and its conjugate momentum must be included in the set of phase-space variables. Furthermore, the action is linear in the acceleration of the curve and possesses a local symmetry-reparametrization invariance-which implies primary constraints in the canonical formalism. These constraints are incorporated into the Hamiltonian through Lagrange multiplier functions that are identified as the components of the acceleration of the curve. The formulation leads to four first-order partial differential equations, one for each canonical variable. With the appropriate choice of parametrization, only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve. To illustrate the formalism, several evolutions of pseudospherical surfaces are discussed.
Renormalization Group Flows of Hamiltonians Using Tensor Networks.
Bal, M; Mariën, M; Haegeman, J; Verstraete, F
2017-06-23
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.180405; S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.110504], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.
A phenomenological Hamiltonian for the Lotka-Volterra problem
Georgian, T. [Corps of Engineers, Omaha, NE (United States); Findley, G.L. [Northeast Louisiana Univ., Monroe, LA (United States)
1996-12-31
We have presented a Hamiltonian theory of phenomenological chemical kinetics. In the present paper, we extend this treatment to the Lotka-Volterra model of sustained oscillations. Our approach begins with the usual definition of an intrinsic reaction coordinate space (x{sub 1},x{sub 2}) for the Lotka-Volterra problem, which leads to the rate equations x{sub 1}=ax{sub 1}-bx{sub 1}x{sub 2}, x{sub 2}=-cx{sub 2}+bx{sub 1}x{sub 2}, with a,b and c being real constants. We thereafter present a Hamiltonian function H(x,y)[y{sub 1} = x{sub 1} and y{sub 2} = x{sub 2}] and an associated holonomic constraint, which give rise to the above rates as half of Hamilton`s equations. We provide trajectories by numerical integration (4th order Runge-Kutta) and show that H(x,y) is a constant of the motion. Finally, issues involved in developing an analytic solution to this problem are discussed.
Effective Hamiltonian for surface states of topological insulator nanotubes
Siu, Zhuo Bin; Tan, Seng Ghee; Jalil, Mansoor B. A.
2017-04-01
In this work we derive an effective Hamiltonian for the surface states of a hollow topological insulator (TI) nanotube with finite width walls. Unlike a solid TI cylinder, a TI nanotube possesses both an inner as well as outer surface on which the states localized at each surface are coupled together. The curvature along the circumference of the nanotube leads to a spatial variation of the spin orbit interaction field experienced by the charge carriers as well as an asymmetry between the inner and outer surfaces of the nanotube. Both of these features result in terms in the effective Hamiltonian for a TI nanotube absent in that of a flat TI thin film of the same thickness. We calculate the numerical values of the parameters for a Bi2Se3 nanotube as a function of the inner and outer radius, and show that the differing relative magnitudes between the parameters result in qualitatively differing behaviour for the eigenstates of tubes of different dimensions.
Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).
Subharmonic solutions for non-autonomous second-order sublinear Hamiltonian systems with p-Laplacian
Zhiyong Wang
2011-10-01
Full Text Available In this article, we study the existence of subharmonic solutions to the non-autonomous second-order sublinear Hamiltonian systems with p-Laplacian. Introducing some kinds of control functions, infinitely many subharmonic solutions are obtained by using the minimax methods in critical point theory. We point out that our results are new even in the case p=2.
Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.
2013-01-01
Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…
Visualizing the zero order basis of the spectroscopic Hamiltonian.
Barnes, George L; Kellman, Michael E
2012-01-14
Recent works have shown that a generalization of the spectroscopic effective Hamiltonian can describe spectra in surprising regions, such as isomerization barriers. In this work, we seek to explain why the effective Hamiltonian is successful where there was reason to doubt that it would work at all. All spectroscopic Hamiltonians have an underlying abstract zero-order basis (ZOB) which is the "ideal" basis for a given form and parameterization of the Hamiltonian. Without a physical model there is no way to transform this abstract basis into a coordinate representation. To this end, we present a method of obtaining the coordinate space representation of the abstract ZOB of a spectroscopic effective Hamiltonian. This method works equally well for generalized effective Hamiltonians that encompass above-barrier multiwell behavior, and standard effective Hamiltonians for the vicinity of a single potential minimum. Our approach relies on a set of converged eigenfunctions obtained from a variational calculation on a potential surface. By making a one-to-one correspondence between the energy eigenstates of the effective Hamiltonian and those of the coordinate space Hamiltonian, a physical representation of the abstract ZOB is calculated. We find that the ZOB basis naturally adjusts its complexity depending on the underlying nature of phase space, which allows spectroscopic Hamiltonians to succeed for systems sampling multiple stationary points.
Hamiltonian realization of power system dynamic models and its applications
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hamiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
Proton radius puzzle in Hamiltonian dynamics
Glazek, Stanislaw D
2014-01-01
Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue equations with the effective Coulomb potential that exhibits a tiny sensitivity to the characteristic momentum-scale of the bound system. The scale dependence is shown to be relevant to the theoretical interpretation of precisely measured lepton-proton bound-state energy levels in terms of a 4 percent difference between the proton radii in muon-proton and electron-proton bound states.
Linear representation of energy-dependent Hamiltonians
Znojil, Miloslav
2004-05-01
Quantum mechanics abounds in models with Hamiltonian operators which are energy-dependent. A linearization of the underlying Schrödinger equation with H= H( E) is proposed here via an introduction of a doublet of separate energy-independent representatives K and L of the respective right and left action of H( E). Both these new operators are non-Hermitian so that our formalism admits a natural extension to non-Hermitian initial H( E)s. Its applicability may range from pragmatic phenomenology and variational calculations (where all the subspace-projected effective operators depend on energy by construction) up to perturbation theory and quasi-exact constructions.
Riccati group invariants of linear hamiltonian systems
Garzia, M. R.; Loparo, K. A.; Martin, C. F.
1983-01-01
The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.
Enumeration of Hamiltonian Cycles in 6-cube
Deza, Michel
2010-01-01
Finding the number 2H6 of directed Hamiltonian cycles in 6-cube is problem 43 in Section 7.2.1.1 of Knuth's ' The Art of Computer Programming'; various proposed estimates are surveyed below. We computed exact value: H6=14,754,666,508,334,433,250,560=6*2^4*217,199*1,085,989*5,429,923. Also the number Aut6 of those cycles up to automorphisms of 6-cube was computed as 147,365,405,634,413,085
Hamiltonian analysis of BHT massive gravity
Blagojević, M.; Cvetković, B.
2011-01-01
We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants ( Λ 0, m 2), our canonical analysis reveals the special role of the condition Λ 0/ m 2 ≠ -1. In this sector, the dimension of the physical phase space is found to be N ∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.
Action-minimizing methods in Hamiltonian dynamics
Sorrentino, Alfonso
2015-01-01
John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as a
Statistical mechanics of Hamiltonian adaptive resolution simulations.
Español, P; Delgado-Buscalioni, R; Everaers, R; Potestio, R; Donadio, D; Kremer, K
2015-02-14
The Adaptive Resolution Scheme (AdResS) is a hybrid scheme that allows to treat a molecular system with different levels of resolution depending on the location of the molecules. The construction of a Hamiltonian based on the this idea (H-AdResS) allows one to formulate the usual tools of ensembles and statistical mechanics. We present a number of exact and approximate results that provide a statistical mechanics foundation for this simulation method. We also present simulation results that illustrate the theory.
The quantization of the Rabi Hamiltonian
Vandaele, Eva R. J.; Arvanitidis, Athanasios; Ceulemans, Arnout
2017-03-01
The Rabi Hamiltonian addresses the proverbial paradigmatic case of a two-level fermionic system coupled to a single bosonic mode. It is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which rationalize the spectrum by relating the solutions to the Juddian baselines. The relationship with Braak’s integrability claim (Braak 2011 Phys. Rev. Lett. 107 100401) is discussed.
Quantum Hamiltonian Identification from Measurement Time Traces
Zhang, Jun; Sarovar, Mohan
2014-08-01
Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.
Hamiltonian BF theory and projected Borromean Rings
Contreras, Ernesto; Leal, Lorenzo
2011-01-01
It is shown that the canonical formulation of the abelian BF theory in D = 3 allows to obtain topological invariants associated to curves and points in the plane. The method consists on finding the Hamiltonian on-shell of the theory coupled to external sources with support on curves and points in the spatial plane. We explicitly calculate a non-trivial invariant that could be seen as a "projection" of the Milnor's link invariant MU(1; 2; 3), and as such, it measures the entanglement of generalized (or projected) Borromeans Rings in the Euclidean plane.
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure—in doing so we try to bring together various fundamental concepts...
Nonabelian N=2 Superstrings: Hamiltonian Structure
Isaev, A P
2009-01-01
We examine the Hamiltonian structure of nonabelian N=2 superstrings models which are the supergroup manifold extensions of N=2 Green-Schwarz superstring. We find the Kac-Moody and Virasoro type superalgebras of the relevant constraints and present elements of the corresponding quantum theory. A comparison with the type IIA Green-Schwarz superstring moving in a general curved 10-d supergravity background is also given. We find that nonabelian superstrings (for d=10) present a particular case of this general system corresponding to a special choices of the background.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
Equivalence of two sets of deformed Calogero-Moser Hamiltonians
Gorbe, T F
2015-01-01
The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BC(n) Ruijsenaars-Schneider-van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found.
Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion
Larsson, Jonas
1986-02-01
Kruskal's asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal's theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L¯) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L¯+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ɛ, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper.
Yuefang Wang; Lihua Huang; Xuetao Liu; Keren Wang
2005-01-01
The Hamiltonian dynamics is adopted to solve the eigenvalue problem for transverse vibrations of axially moving strings. With the explicit Hamiltonian function the canonical equation of the free vibration is derived. Non-singular modal functions are obtained through a linear, symplectic eigenvalue analysis, and the symplectic-type orthogonality conditions of modes are derived. Stability of the transverse motion is examined by means of analyzing the eigenvalues and their bifurcation, especially for strings transporting with the critical speed. It is pointed out that the motion of the string does not possess divergence instability at the critical speed due to the weak interaction between eigenvalue pairs. The expansion theorem is applied with the non-singular modal functions to solve the displacement response to free and forced vibrations. It is demonstrated that the modal functions can be used as the base functions for solving linear and nonlinear vibration problems.
Hamiltonian Cycles in Regular 2-Connected Claw-Free Graphs
李明楚
2003-01-01
A known result by Jackson Bill is that every 2-connected k-regular graph on at most 3k vertices is Hamiltonian. In this paper,it is proved that every 2-connected k-regular claw-free graph on at most 5k(k≥10)vertices is Hamiltonian. Moreover, the bound 5k is best possible. A counterexample of a 2-connected k-regular claw-free non-Hamiltonian graph on 5k+1 vertices is given, and it is conjectured that every 3-connected k-regular claw-free graph on at most 12k-7 vertices is Hamiltonian.
Covariant hamiltonian spin dynamics in curved space–time
D' Ambrosi, G., E-mail: gdambros@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Satish Kumar, S., E-mail: satish@lorentz.leidenuniv.nl [Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands); Holten, J.W. van, E-mail: t32@nikhef.nl [Nikhef, Science Park 105, Amsterdam (Netherlands); Lorentz Institute, Leiden University, Niels Bohrweg 2, Leiden (Netherlands)
2015-04-09
The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space–time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern–Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
Covariant hamiltonian spin dynamics in curved space-time
d'Ambrosi, G; van Holten, J W
2015-01-01
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
How is Lorentz invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-07-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
How is Lorentz Invariance encoded in the Hamiltonian?
Kajuri, Nirmalya
2016-01-01
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
A New Scheme of Integrability for (bi)Hamiltonian PDE
De Sole, Alberto; Kac, Victor G.; Valeri, Daniele
2016-10-01
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.
Hamiltonian realization of power system dynamic models and its applications
MA Jin; MEI ShengWei
2008-01-01
Power system is a typical energy system. Because Hamiltonian approaches are closely related to the energy of the physical system, they have been widely re-searched in recent years. The realization of the Hamiltonian structure of the nonlinear dynamic system is the basis for the application of the Hamiltonian methods. However, there have been no systematically investigations on the Ham-iltonian realization for different power system dynamic models so far. This paper researches the Hamiltonian realization in power systems dynamics. Starting from the widely used power system dynamic models, the paper reveals the intrinsic Hamiltonian structure of the nonlinear power system dynamics and also proposes approaches to formulate the power system Hamiltonian structure. Furthermore, this paper shows the application of the Hemiltonian structure of the power system dynamics to design non-smooth controller considering the nonlinear ceiling effects from the real physical limits. The general procedure to design controllers via the Hamiltonian structure is also summarized in the paper. The controller design based on the Hamiltonian structure is a completely nonlinear method and there is no lin-earization during the controller design process. Thus, the nonlinear characteristics of the dynamic system are completely kept and fully utilized.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
Bagarello, Fabio
2011-01-01
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\\dagger]=0$ and $x^\\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
Solutions of the Bohr Hamiltonian, a compendium
Fortunato, L.
2005-10-01
The Bohr Hamiltonian, also called collective Hamiltonian, is one of the cornerstones of nuclear physics and a wealth of solutions (analytic or approximated) of the associated eigenvalue equation have been proposed over more than half a century (confining ourselves to the quadrupole degree of freedom). Each particular solution is associated with a peculiar form for the V(β,γ) potential. The large number and the different details of the mathematical derivation of these solutions, as well as their increased and renewed importance for nuclear structure and spectroscopy, demand a thorough discussion. It is the aim of the present monograph to present in detail all the known solutions in γ-unstable and γ-stable cases, in a taxonomic and didactical way. In pursuing this task we especially stressed the mathematical side leaving the discussion of the physics to already published comprehensive material. The paper contains also a new approximate solution for the linear potential, and a new solution for prolate and oblate soft axial rotors, as well as some new formulae and comments. The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling of bands in triaxial nuclei.
Dirac Hamiltonian with superstrong Coulomb field
Voronov, B L; Tyutin, I V
2006-01-01
We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist for charge values exceeding the so-called critical charge with Z=137 based on the fact that the standard expression for energy eigenvalues yields complex values at overcritical charges. We show that from the mathematical standpoint, there is no problem in defining a self-adjoint Hamiltonian for any value of charge. What is more, the transition through the critical charge does not lead to any qualitative changes in the mathematical description of the system. A specific feature of overcritical charges is the nonuniqueness of the self-adjoint Hamiltonian, but this nonuniqueness is also characteristic for charge values less than the critical one (and larger than the subcritical charge with Z=118). We present the spectra and (generalized) eigenfunctions for all self-adjoint Hamilt...
A Hamiltonian Five-Field Gyrofluid Model
Keramidas Charidakos, Ioannis; Waelbroeck, Francois; Morrison, Philip
2015-11-01
Reduced fluid models constitute versatile tools for the study of multi-scale phenomena. Examples include magnetic islands, edge localized modes, resonant magnetic perturbations, and fishbone and Alfven modes. Gyrofluid models improve over Braginskii-type models by accounting for the nonlocal response due to particle orbits. A desirable property for all models is that they not only have a conserved energy, but also that they be Hamiltonian in the ideal limit. Here, a Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of electron and ion densities, the parallel component of ion and electron velocities and ion temperature. Quasineutrality and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models. This work was funded by U.S. DOE Contract No. DE-FG02-04ER-54742.
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Bigravity in Kuchar's Hamiltonian formalism. 1. The General Case
Soloviev, Vladimir O
2013-01-01
The Hamiltonian formalism of bigravity and bimetric theories is constructed for the general form of potential between two metrics. It is natural to study the role played by the lapse and shift functions in theories with two metrics on the base of Kuchar's approach because then they do not depend on the choice of space-time coordinate frame. The algebra of first class constraints is derived in Dirac brackets constructed from the second class constraints. It is the celebrated algebra of the hypersurface deformations. Fixing one of the metrics we obtain a bimetric theory without any first class constrains. Then we can use the symmetries of the background metric to construct conserved quantities looking ultralocally when written through the potential. The special case of potential providing the less number for degrees of freedom will be treated in the companion paper.
Model Hamiltonian for the conductivity oscillations of magnetic multilayers
Weissmann, Mariana; Llois, Ana Maria; Kiwi, Miguel; Ramirez, Ricardo
1997-03-01
The behavior of the electrical conductivity as a function of layer thickness of the superlattice systems Ni/Co, Ni/Cu and Pd/Ag is studied. Experimentally an oscillatory dependence was found for the first two, while the latter exhibited a monotonous behavior. In our previous calculations we found that, in these superlattices, the current is carried by the sp--character electrons, which are quite insensitive to the interfaces. Therefore, to interpret the experimentally observed resistivity oscillations, we suggest a scattering mechanism of these carriers against d--character quantum well states that are present in only one of the superlattice materials, when the well state energy is close to E_F. To explore the validity of this mechanism we have put forward a model Hamiltonian which, for reasonable values of the parameters, leads to results in good agreement with experiments.
Hamiltonian formulation of time-dependent plausible inference
Davis, Sergio
2014-01-01
Maximization of the path information entropy is a clear prescription for performing time-dependent plausible inference. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its associated Fokker-Planck equation. The connections unveiled between the maximization of path entropy and the Langevin/Fokker-Planck equations imply that missing information about the phase space coordinate never decreases in time, a purely information-theoretical version of the Second Law of Thermodynamics. All of these results are independent of any physical assumptions, and thus valid for any generalized coordinate as a function of time, or any other parameter. This reinforces the view that the Second Law is a fundamental property of ...
On the Convexity of the KdV Hamiltonian
Kappeler, Thomas; Maspero, Alberto; Molnar, Jan; Topalov, Peter
2016-08-01
Motivated by perturbation theory, we prove that the nonlinear part {H^{*}} of the KdV Hamiltonian {H^{kdv}}, when expressed in action variables {I = (In)_{n ≥slant 1}}, extends to a real analytic function on the positive quadrant {ℓ2+({N})} of {ℓ2({N})} and is strictly concave near {0}. As a consequence, the differential of {H^{*}} defines a local diffeomorphism near 0 of {ℓ_{{C}}2({N})}. Furthermore, we prove that the Fourier-Lebesgue spaces {{F}{L}^{s,p}} with {-1/2 ≤slant s ≤slant 0} and {2 ≤slant p KdV-Birkhoff coordinates. In particular, it means that {ℓ2_+({N})} is the space of action variables of the underlying phase space {{F}{L}^{-1/2,4}} and that the KdV equation is globally in time {C0}-well-posed on {{F}{L}^{-1/2,4}}.
Hamiltonian light-front field theory and quantum chromodynamics
Perry, R J
1994-01-01
Light-front coordinates offer a scenario in which a constituent picture of hadron structure can emerge from QCD, after several difficulties are addressed. Field theoretic difficulties force us to introduce cutoffs that violate Lorentz covariance and gauge invariance, and a new renormalization group formalism based on a similarity transformation is used with coupling coherence to fix cuonterterms that restore these symmetries. The counterterms contain functions of longitudinal momentum fractions that severely complicate renormalization, but they also offer possible resolutions of apparent contradictions between the constituent picture and QCD. The similarity transformation and coupling coherence are applied to QED; and it is shown that the resultant Hamiltonian leads to standard lowest order bound state results, with the Coulomb interaction emerging naturally. The same techniques are applied to QCD and with physically motivated assumptions it is shown that a simple confinement mechanism appears. Bare `masses' ...
Many-body Hamiltonian with screening parameter and ionization energy
Andrew Das Arulsamy
2010-04-01
We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature (0) and the ionization energy (). We show that the existence of this total energy eigenvalue, 0 ± , does not violate the Coulombian atomic system. Since there is no equivalent known Hamilton operator that corresponds quantitatively to , we employ the screened Coulomb potential operator (Yukawa-type), which is a function of this ionization energy to analytically calculate the screening parameter () of a neutral helium atom in the ground state. In addition, we also show that the energy level splitting due to spin-orbit coupling is inversely proportional to eigenvalue, which is also important in the field of spintronics.
Hamiltonians and variational principles for Alfvén simple waves
Webb, G. M.; Hu, Q.; le Roux, J. A.; Dasgupta, B.; Zank, G. P.
2012-01-01
The evolution equations for the magnetic field induction B with the wave phase for Alfvén simple waves are expressed as variational principles and in the Hamiltonian form. The evolution of B with the phase (which is a function of the space and time variables) depends on the generalized Frenet-Serret equations, in which the wave normal n (which is a function of the phase) is taken to be tangent to a curve X, in a 3D Cartesian geometry vector space. The physical variables (the gas density, fluid velocity, gas pressure and magnetic field induction) in the wave depend only on the phase. Three approaches are developed. One approach exploits the fact that the Frenet equations may be written as a 3D Hamiltonian system, which can be described using the Nambu bracket. It is shown that B as a function of the phase satisfies a modified version of the Frenet equations, and hence the magnetic field evolution equations can be expressed in the Hamiltonian form. A second approach develops an Euler-Poincaré variational formulation. A third approach uses the Frenet frame formulation, in which the hodograph of B moves on a sphere of constant radius and uses a stereographic projection transformation due to Darboux. The equations for the projected field components reduce to a complex Riccati equation. By using a Cole-Hopf transformation, the Riccati equation reduces to a linear second order differential equation for the new variable. A Hamiltonian formulation of the second order differential equation then allows the system to be written in the Hamiltonian form. Alignment dynamics equations for Alfvén simple waves give rise to a complex Riccati equation or, equivalently, to a quaternionic Riccati equation, which can be mapped onto the Riccati equation obtained by stereographic projection.
New relativistic Hamiltonian: the angular magnetoelectric coupling
Paillard, Charles; Mondal, Ritwik; Berritta, Marco; Dkhil, Brahim; Singh, Surendra; Oppeneer, Peter M.; Bellaiche, Laurent
2016-10-01
Spin-Orbit Coupling (SOC) is a ubiquitous phenomenon in the spintronics area, as it plays a major role in allowing for enhancing many well-known phenomena, such as the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, the Rashba effect, etc. However, the usual expression of the SOC interaction ħ/4m2c2 [E×p] • σ (1) where p is the momentum operator, E the electric field, σ the vector of Pauli matrices, breaks the gauge invariance required by the electronic Hamiltonian. On the other hand, very recently, a new phenomenological interaction, coupling the angular momentum of light and magnetic moments, has been proposed based on symmetry arguments: ξ/2 [r × (E × B)] M, (2) with M the magnetization, r the position, and ξ the interaction strength constant. This interaction has been demonstrated to contribute and/or give rise, in a straightforward way, to various magnetoelectric phenomena,such as the anomalous Hall effect (AHE), the anisotropic magnetoresistance (AMR), the planar Hall effect and Rashba-like effects, or the spin-current model in multiferroics. This last model is known to be the origin of the cycloidal spin arrangement in bismuth ferrite for instance. However, the coupling of the angular momentum of light with magnetic moments lacked a fundamental theoretical basis. Starting from the Dirac equation, we derive a relativistic interaction Hamiltonian which linearly couples the angular momentum density of the electromagnetic (EM) field and the electrons spin. We name this coupling the Angular MagnetoElectric (AME) coupling. We show that in the limit of uniform magnetic field, the AME coupling yields an interaction exactly of the form of Eq. (2), thereby giving a firm theoretical basis to earlier works. The AME coupling can be expressed as: ξ [E × A] • σ (3) with A being the vector potential. Interestingly, the AME coupling was shown to be complementary to the traditional SOC, and together they restore the gauge invariance of the
Hamiltonian structure of an operator valued extension of Super KdV equations
Restuccia, A
2014-01-01
An extension of the super Korteweg-de Vries integrable system in terms of operator valued functions is obtained. In particular the extension contains the $N=1$ Super KdV and coupled systems with functions valued on a symplectic space. We introduce a Miura transformation for the extended system and obtain its hamiltonian structure. We also obtain an extended Gardner transformation which allows to find an infinite number of conserved quantities of the extended system.
Symmetry and reduction in implicit generalized Hamiltonian systems
Blankenstein, G.; Schaft, van der A.J.
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this a
Symmetry and Reduction in Implicit Generalized Hamiltonian Systems
Blankenstein, G.; Schaft, A.J. van der
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding conserved quantities. Main features
Non-self-adjoint hamiltonians defined by Riesz bases
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
HAMILTONIAN DECOMPOSITION OF COMPLETE BIPARTITE r-HYPERGRAPHS
吉日木图; 王建方
2001-01-01
In [1] the concepts of paths and cycles of a hypergraph were introduced. In this paper, we give the concepts for bipartite hypergraph and Hamiltonian paths and cycles of a hypergraph,and prove that the complete bipartite 3-hypergraph with q vertices in each part is Hamiltonian decomposable where q is a prime.
THE HAMILTONIAN SYSTEMS OF THE LCZ HIERARCHY BY NONLINEARIZATION
Li Lu
2000-01-01
In this paper, we first search for the Hamiltonian structure of LCZ hierarchy by use of a trace identity. Then we determine a higher-order constraint condition between the potentials and the eigenfunctions of the LCZ spectral problem, and under this constraint condition, the Lax pairs of LCZ hierarchy are all nonlinearized into the finite-dimensional integrable Hamiltonian systems in Liouville sense.
Integrability and Non-integrability of Hamiltonian Normal Forms
Verhulst, Ferdinand
2015-01-01
This paper summarizes the present state of integrability of Hamiltonian normal forms and it aims at characterizing non-integrable behaviour in higher-dimensional systems. Non-generic behaviour in Hamiltonian systems can be a sign of integrability, but it is not a conclusive indication. We will discu
A SUFFICIENT CONDITION FOR HAMILTONIAN CYCLES IN BIPARTITE TOURNAMENTS
无
2007-01-01
In this paper, we present a new sufficient condition on degrees for a bipartite tournament to be Hamiltonian, that is, if an n × n bipartite tournament T satisfies the condition W(n - 3), then T is Hamiltonian, except for four exceptional graphs. This result is shown to be best possible in a sense.
Bifurcations in Hamiltonian systems with a reflecting symmetry
Bosschaert, M.; Hanssmann, H.
2011-01-01
A reflecting symmetry q 7→ −q of a Hamiltonian system does not leave the symplectic structure dq∧dp invariant and is therefore usually asso- ciated with a reversible Hamiltonian system. However, if q 7→ −q leads to H 7→ −H, then the equations of motion are invariant under the re- flection. This impo
Quantum System Identification: Hamiltonian Estimation using Spectral and Bayesian Analysis
Schirmer, S G
2009-01-01
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation procedure is proposed and evaluated for a model system where a-priori information about the Hamiltonian's structure is available.
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
Distributed port-Hamiltonian formulation of infinite dimensional systems
Macchelli, Alessandro; Schaft, van der Arjan J.; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-va
Distributed Port-Hamiltonian Formulation of Innite Dimensional Systems
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling and control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-va
Port controlled Hamiltonian representation of distributed parameter systems
Maschke, B.M.; van der Schaft, Arjan
2000-01-01
A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. This port controlled
Port-Hamiltonian approach to deployment on a line
Vos, Ewoud; Scherpen, Jacquelien M.A.; van der Schaft, Abraham
2012-01-01
In this talk we present a port-Hamiltonian approach to the deployment on a line of a robotic sensor network (see e.g. [3] for related work). Using the port-Hamiltonian modelling framework has some clear benefits. Including physical interpretation of the model, insight in the system’s energy and
On the minimization of Hamiltonians over pure Gaussian states
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Port-Hamiltonian approach to deployment on a line
Vos, Ewoud; Scherpen, Jacquelien M.A.; van der Schaft, Abraham
2012-01-01
In this talk we present a port-Hamiltonian approach to the deployment on a line of a robotic sensor network (see e.g. [3] for related work). Using the port-Hamiltonian modelling framework has some clear benefits. Including physical interpretation of the model, insight in the system’s energy and stru
The Group of Hamiltonian Automorphisms of a Star Product
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
A Quantum Algorithm for the Hamiltonian NAND Tree
Farhi, E; Gutmann, S
2007-01-01
We give a quantum algorithm for the NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt(N)*sqrt(logN). We also show a lower bound of sqrt(N) for the NAND tree problem in the Hamiltonian oracle model.
Weak Hamiltonian, CP Violation and Rare Decays
Buras, Andrzej J
1998-01-01
These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dimensions of operators and anomalous dimension matrices. We elaborate on the renormalzation scheme and renormalization scale dependences and their cancellations in physical amplitudes. In particular we discuss the issue of gamma-5 in D-dimensions and the role of evanescent operators in the calculation of two-loop anomalous dimensions. We present an explicit calculation of the 6 times 6 one-loop anomalous dimension matrix involving current-current and QCD-penguin operators and we give some hints how to properly calculate two-loop anomalous dimensions of these operators. In the phenonomenological part of these lectures we discuss in detail: CKM matrix, the unitarity triangle and its determination, two-body non-leptonic...
Geometric solitons of Hamiltonian flows on manifolds
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM
孙雁; 周钢; 刘正兴
2003-01-01
It is not convenient to solve those engineering problems defined in an infinitefield by using FEM. An infinite area can be divided into a regular infinite external area anda finite internal area. The finite internal area was dealt with by the FEM and the regularinfinite external area was settled in a polar coordinate. All governing equations weretransformed into the Hamiltonian system. The methods of variable separation andeigenfunction expansion were used to derive the stiffness matrix of a new infinite analyticalelement. This new element, like a super finite element, can be combined with commonlyused finite elements. The proposed method was verified by numerical case studies. Theresults show that the preparation work is very simple, the infinite analytical element has ahigh precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
Boundary Liouville Theory: Hamiltonian Description and Quantization
Harald Dorn
2007-01-01
Full Text Available The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator $e^varphi$ in terms of free field exponentials is constructed in the hyperbolic sector.
Mixing properties of stochastic quantum Hamiltonians
Onorati, E; Kliesch, M; Brown, W; Werner, A H; Eisert, J
2016-01-01
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathema...
Hamiltonian approach to GR. Pt. 2. Covariant theory of quantum gravity
Cremaschini, Claudio [Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Opava (Czech Republic); Tessarotto, Massimo [University of Trieste, Department of Mathematics and Geosciences, Trieste (Italy); Faculty of Philosophy and Science, Silesian University in Opava, Institute of Physics, Opava (Czech Republic)
2017-05-15
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton-Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton-Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant. (orig.)
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
Pan, Yu; James, Matthew R. [Australian National University, Research School of Engineering, Canberra (Australia); Miao, Zibo [The University of Melbourne, Department of Electrical and Electronic Engineering, Melbourne (Australia); Amini, Nina H. [CNRS, Laboratoire des Signaux et Systemes (L2S) Supelec, Gif-Sur-Yvette (France); Ugrinovskii, Valery [University of New South Wales at ADFA, School of Engineering and Information Technology, Canberra (Australia)
2015-12-15
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Yu, Xiongjie; Pekker, David; Clark, Bryan K.
2017-01-01
A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.
Lopez-Moreno, Enrique; Grether, M; Velazquez, Victor, E-mail: elm@hp.fciencias.unam.mx [Facultad de Ciencias, Departamento de Fisica, Universidad Nacional Autonoma de Mexico, Cd. Universitaria, Circuito Exterior, 04510 Mexico DF (Mexico)
2011-11-25
A general spin system with a nonaxially symmetric Hamiltonian containing J{sub x}, J{sub z}-linear and J{sub z}-quadratic terms, widely used in many-body fermionic and bosonic systems and in molecular magnetism, is considered for the variations of general parameters describing intensity interaction changes of each of its terms. For this model Hamiltonian, a semiclassical energy surface (ES) is obtained by means of the coherent-state formalism. An analysis of this ES function, based on catastrophe theory, determines the separatrix in the control parameter space of the system Hamiltonian: the loci of singularities representing semiclassical phase transitions. Here we show that distinct regions of qualitatively different spectrum structures, as well as a singular behavior of quantum states, are ruled by this separatrix: here we show that the separatrix not only describes ground-state singularities, which have been associated with quantum phase transitions, but also reveals the structure of the excited spectrum, distinguishing different quantum phases within the parameter space. Finally, we consider magnetic susceptibility and heat capacity of the system at finite temperature, in order to study thermal properties and thermodynamical phase transitions in the perspective of the separatrix of this Hamiltonian system. (paper)
Action and Index Spectra and Periodic Orbits in Hamiltonian Dynamics
Ginzburg, Viktor L
2008-01-01
The main theme of this paper is the connection between the existence of infinitely many periodic orbits for a Hamiltonian system and the behavior of its action or index spectrum under iterations. We use the action and index spectra to show that any Hamiltonian diffeomorphism of a closed, rational manifold with zero first Chern class has infinitely many periodic orbits and that, for a general rational manifold, the number of geometrically distinct periodic orbits is bounded from below by the ratio of the minimal Chern number and half of the dimension. These generalizations of the Conley conjecture follow from another result proved here asserting that a Hamiltonian diffeomorphism with a symplectically degenerate maximum on a closed rational manifold has infinitely many periodic orbits. We also show that for a broad class of manifolds and/or Hamiltonian diffeomorphisms the minimal action--index gap remains bounded for some infinite sequence of iterations and, as a consequence, whenever a Hamiltonian diffeomorphi...
Remarks on the Lagrangian representation of bi-Hamiltonian equations
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David
2015-01-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradski ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Hamiltonian analysis of higher derivative scalar-tensor theories
Langlois, David; Noui, Karim
2016-07-01
We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Wu-hwan Jong
2013-11-01
Full Text Available We proved a parameterized KAM theorem in Hamiltonian system which has differentiable Hamiltonian without action-angle coordinates. It is a generalization of the result of [20] that deals with real analytic Hamiltonians.
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians
Patel, Apoorva; Priyadarsini, Anjani
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.
Yu, Pei; Han, Maoan
2013-04-01
In this paper, we show that a Z2-equivariant 3rd-order Hamiltonian planar vector fields with 3rd-order symmetric perturbations can have at least 10 limit cycles. The method combines the general perturbation to the vector field and the perturbation to the Hamiltonian function. The Melnikov function is evaluated near the center of vector field, as well as near homoclinic and heteroclinic orbits.
An effective Hamiltonian approach to quantum random walk
Sarkar, Debajyoti; Paul, Niladri; Bhattacharya, Kaushik; Ghosh, Tarun Kanti
2017-03-01
In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are generators of time translations. Then an attempt has been made to generalize the techniques to higher dimensions. We find that the Hamiltonian can be written as the sum of a Weyl Hamiltonian and a Dirac comb potential. The time evolution operator obtained from this prescribed Hamiltonian is in complete agreement with that of the standard approach. But in higher dimension we find that the time evolution operator is additive, instead of being multiplicative (see Chandrashekar, Sci. Rep. 3, 2829 (18)). We showed that in the case of two-step walk, the time evolution operator effectively can have multiplicative form. In the case of a square lattice, quantum walk has been studied computationally for different coins and the results for both the additive and the multiplicative approaches have been compared. Using the graphene Hamiltonian, the walk has been studied on a graphene lattice and we conclude the preference of additive approach over the multiplicative one.
Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2
Alekseev, A Yu; Schomerus, V; Grosse, H; Schomerus, V
1994-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \\cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathe- matically rigorous definition of the algebra of observables \\A_{CS} of the Chern Simons model. It is a *-algebra of ``functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional \\omega (``integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly \\cite{FoRo}, the algebra \\A_{CS} provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verl...
Unconstrained Hamiltonian formulation of low energy QCD
Pavel Hans-Peter
2014-04-01
Full Text Available Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case. The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons, and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate
Landau levels in 2D materials using Wannier Hamiltonians obtained by first principles
Lado, J. L.; Fernández-Rossier, J.
2016-09-01
We present a method to calculate the Landau levels and the corresponding edge states of two dimensional (2D) crystals using as a starting point their electronic structure as obtained from standard density functional theory (DFT). The DFT Hamiltonian is represented in the basis of maximally localized Wannier functions. This defines a tight-binding Hamiltonian for the bulk that can be used to describe other structures, such as ribbons, provided that atomic scale details of the edges are ignored. The effect of the orbital magnetic field is described using the Peierls substitution in the hopping matrix elements. Implementing this approach in a ribbon geometry, we obtain both the Landau levels and the dispersive edge states for a series of 2D crystals, including graphene, Boron Nitride, MoS2, Black Phosphorous, Indium Selenide and MoO3. Our procedure can readily be used in any other 2D crystal, and provides an alternative to effective mass descriptions.
Martínez, Y. P.; Vidal, C.
2016-12-01
In this paper we study the global dynamics of the Hamiltonian systems x ˙ =Hy (x , y), y ˙ = -Hx (x , y), where the Hamiltonian function H has the particular form H (x , y) =y2 / 2 + P (x) / Q (x), P (x) , Q (x) ∈ R [ x ] are polynomials, in particular H is the sum of the kinetic and a rational potential energies. Firstly, we provide the normal forms by a suitable μ-symplectic change of variables. Then, the global topological classification of the phase portraits of these systems having canonical forms in the Poincaré disk in the cases where degree (P) = 0 , 1 , 2 and degree (Q) = 0 , 1 , 2 are studied as a function of the parameters that define each polynomial. We use a blow-up technique for finite equilibrium points and the Poincaré compactification for the infinite equilibrium points. Finally, we show some applications.
A finite-temperature Hartree-Fock code for shell-model Hamiltonians
Bertsch, G. F.; Mehlhaff, J. M.
2016-10-01
The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.
Generalized Hamiltonian Systems on a Poisson Product Manifold%泊松流形中的一般哈密尔顿系统
王红
2005-01-01
We firstly intoruduced a kind of special functions and a kind of special Poisson bracket on a product manifold,then give a kind of special generalized Hamiltonian vector fields by using the special Poisson bracket.Moreover,we give a method to compose a new generalized Hamiltonian system on the Poisson product manifold by using two known generalized Hamitonian systems on the factor Poisson manifolds.We also discuss the conservative properties of the new composed generalized Hamiltonian systems as well as the relation between the Poisson mapping on the Poisson product manifold and that on the factor Poisson manifolds.
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
On the minimization of Hamiltonians over pure Gaussian states
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown...... that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only terms that can be interpreted as quasiparticles excitations. We propose to call this fact Beliaev's Theorem, since to our knowledge it was mentioned for the first time in a paper...
A KAM-type Theorem for Generalized Hamiltonian Systems
LIU BAI-FENG; ZHU WEN-ZHUANG; XU LE-SHUN; Li Yong
2009-01-01
In this paper we mainly concern the persistence of lower-dimensional invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensionai tori might be elliptic, hyperbolic, or of mixed type.
A cohomological obstruction for global quasi-bi-Hamiltonian fields
Rakotondralambo, Joseph, E-mail: joseph.rakotondralambo@unimes.f [Departement de Mathematiques et Informatique, Faculte des Sciences, Universite d' Antananarivo (Madagascar)
2011-02-14
We introduce the notion of integrating factor for a 1-form which is an inner product of a vector fields and a 2-form, and the notion of weakly bi-Hamiltonian field also, which is locally quasi-bi-Hamiltonian. A cohomological class in some first cohomology space is associated to such vector fields when this is weakly bi-Hamiltonian and defined relatively to the above 1-form. This class is a cohomological obstruction to the existence of a global integrating factor for the 1-form.
An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
Masterov, Ivan
2015-01-01
Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [Acta Phys. Polon. B 36 (2005) 2115] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N=2 supersymmetric Pais-Uhlenbeck oscillator.
An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
Masterov, Ivan
2016-01-01
Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N = 2 supersymmetric Pais-Uhlenbeck oscillator.
Hamiltonian dynamics of several rigid bodies interacting with point vortices
Weissmann, Steffen
2013-01-01
We introduce a Hamiltonian description for the dynamics of several rigid bodies interacting with point vortices in an inviscid, incompressible fluid. We adopt the idea of Vankerschaver et al. (2009) to derive the Hamiltonian formulation via symplectic reduction of a canonical Hamiltonian system on a principle fibre bundle. On the reduced phase space we determine the magnetic symplectic form directly, without resorting to the machinery of mechanical connections on principle fibre bundles. We derive the equations of motion for the general case, and also for the special Lie-Poisson case of a single rigid body and zero total vorticity. Finally we give a partly degenerate Lagrangian formulation for the system.
New Hamiltonian constraint operator for loop quantum gravity
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Diagonal representation for a generic matrix valued quantum Hamiltonian
Gosselin, Pierre [Universite Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF UFR de Mathematiques, BP74, Saint Martin d' Heres Cedex (France); Mohrbach, Herve [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, ICPMB-FR CNRS 2843, Metz Cedex 3 (France)
2009-12-15
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a running variable are introduced. This method leads to a formal compact expression for the diagonal Hamiltonian which can be expanded in a power series of the Planck constant. In particular, we provide an explicit expression for the diagonal representation of a generic Hamiltonian to the second order in the Planck constant. This result is applied, as a physical illustration, to Dirac electrons and neutrinos in external fields. (orig.)
Robust H∞ Control of Hamiltonian System with Uncertainty
薛安成; 梅生伟; 胡伟; 周原
2003-01-01
This paper investigates the robust H∞ problem for a class of generalized forced Hamiltonian systems with uncertainties. The robust L2-gain was proved for the Hamiltonian with a sufficient condition for stable control of multimachine power systems expressed as a matrix algebraic inequality. A similar sufficient condition was then extended to the robust H∞ control of Hamiltonian systems to construct the state feedback H∞ control law. A numerical example is given to verify the validity of the proposed control scheme, which shows the effectiveness and promising application of the method.
Covariant Hamiltonian for the electromagnetic two-body problem
De Luca, Jayme
2005-09-01
We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.
Entangling capacities of noisy non-local Hamiltonians
Bandyopadhyay, S; Bandyopadhyay, Somshubhro; Lidar, Daniel A.
2003-01-01
We show that intrinsic Gaussian fluctuations in system control parameters impose limits on the ability of non-local (exchange) Hamiltonians to generate entanglement in the presence of mixed initial states. We find three equivalence classes. For the Ising and XYZ models there are qualitatively distinct sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the presence of noise, thus potentially reducing the need for quantum error correction.
Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms
Sorrentino, Alfonso
2010-01-01
In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather's $\\beta$ function, thus providing a negative answer to a question asked by K. Siburg in \\cite{Siburg1998}. However, we show that equality holds if one considers the asymptotic distance defined in \\cite{Viterbo1992}.
Alternative solution of the gamma-rigid Bohr Hamiltonian in minimal length formalism
Alimohammadi, M.; Hassanabadi, H.
2017-01-01
The Bohr-Mottelson Hamiltonian on γ-rigid regime has been extended to the minimal length formalism for the infinite square well potential and the corresponding wave functions as well as the spectra are obtained. The effect of minimal length on energy spectra is studied via various figures and tables and numerical calculations are included for some nuclei and the results are compared with other results and existing experimental data.
Davydov-Chaban Hamiltonian in presence of time-dependent potential
Sobhani, Hadi; Hassanabadi, Hassan
2016-09-01
In this article, we have investigated collective effects of atomic nuclei in presence of a time-dependent potential in Davydov-Chaban Hamiltonian. Since such potential has an explicit time-dependency, in order to obtain the wave function of considered system, we should face with time-dependent Schrödinger equation. Obtaining the wave function could be possible using Lewis-Riesenfeld dynamical invariant method. Appropriate dynamical invariant has been constructed after determining the wave functions and values, the wave function will obtain.
Time-dependent constrained Hamiltonian systems and Dirac brackets
Leon, Manuel de [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Madrid (Spain); Marrero, Juan C. [Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands (Spain); Martin de Diego, David [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, Madrid (Spain)
1996-11-07
In this paper the canonical Dirac formalism for time-dependent constrained Hamiltonian systems is globalized. A time-dependent Dirac bracket which reduces to the usual one for time-independent systems is introduced. (author)
INTEGRABLE COUPLINGS OF THE TB HIERARCHY AND ITS HAMILTONIAN STRUCTURE
无
2008-01-01
In this paper,we obtain integrable couplings of the TB hierarchy using the new subalgebra of the loop algebra A_3.Then the Hamiltonian structure of the above system is given by the quadratic-form identity.
Periodic equatorial water flows from a Hamiltonian perspective
Ionescu-Kruse, Delia; Martin, Calin Iulian
2017-04-01
The main result of this paper is a Hamiltonian formulation of the nonlinear governing equations for geophysical periodic stratified water flows in the equatorial f-plane approximation allowing for piecewise constant vorticity.
Rotationally Invariant Hamiltonians for Nuclear Spectra Based on Quantum Algebras
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2002-01-01
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational nuclear spectra is explicitly proved and a connection of this Hamiltonian to the formalisms of Amal'sky and Harris is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITO) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved, a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced, and its connection to the Harris formalism is established. Numerical tests in a series of Th isotopes are provided.
ORDERED ANALYTIC REPRESENTATION OF PDES BY HAMILTONIAN CANONICAL SYSTEM
ZhengYu; ChenYong
2002-01-01
Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed. Meanwhile some related necessary and sufficient conditions are obtained.
Spin filtering on a ring with Rashba hamiltonian
Harmer, M.
2007-01-01
We consider a quantum graph consisting of a ring with Rashba hamiltonian and an arbitrary number of semi-infinite wires attached. We describe the scattering matrix for this system and investigate spin filtering for a three terminal device.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Construction of Lagrangians and Hamiltonians from the Equation of Motion
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
Hamiltonian Formalism of the Derivative Nonlinear Schrodinger Equation
CAI Hao; LIU Feng-Min; HUANG Nian-Ning
2003-01-01
A particular form of poisson bracket is introduced for the derivative nonlinear Schrodinger (DNLS) equation.And its Hamiltonian formalism is developed by a linear combination method. Action-angle variables are found.
A Hamiltonian Algorithm for Singular Optimal LQ Control Systems
Delgado-Tellez, M
2012-01-01
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the well-known Rabier-Rheinhboldt constraints algorithm used to solve differential-algebraic equations. Its geometrical content is exploited fully by implementing a Hamiltonian extension of it which is closer to Gotay-Nester presymplectic constraint algorithm used to solve singular Hamiltonian systems. Thus, given an optimal control problem whose optimal feedback is given in implicit form, a consistent set of equations is obtained describing the first order differential conditions of Pontryaguine's Maximum Principle. Such equations are shown to be Hamiltonian and the set of first class constraints corresponding to controls that are not determined, are obtained explicitly. The strength of the algorithm is shown by exhibiting a numerical implementation with partial feedback on the c...
Existence of solutions to fractional Hamiltonian systems with combined nonlinearities
Ziheng Zhang
2016-01-01
Full Text Available This article concerns the existence of solutions for the fractional Hamiltonian system $$\\displaylines{ - _tD^{\\alpha}_{\\infty}\\big(_{-\\infty}D^{\\alpha}_{t}u(t\\big -L(tu(t+\
On the Edge-Hyper-Hamiltonian Laceability of Balanced Hypercubes
Cao Jianxiang
2016-11-01
Full Text Available The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E, we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v, there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn is edge-hy per- Hamiltonian laceable.
Spin filtering on a ring with Rashba hamiltonian
Harmer, M
2006-01-01
We consider a quantum graph consisting of a ring with Rashba hamiltonian and an arbitrary number of semi-infinite wires attached. We describe the scattering matrix for this system and investigate spin filtering for a three terminal device.
Matrix factorization method for the Hamiltonian structure of integrable systems
S Ghosh; B Talukdar; S Chakraborti
2003-07-01
We demonstrate that the process of matrix factorization provides a systematic mathematical method to investigate the Hamiltonian structure of non-linear evolution equations characterized by hereditary operators with Nijenhuis property.
Cliffordized NAC supersymmetry and PT-symmetric Hamiltonians
Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: toppan@cbpf.br
2007-07-01
It is shown that non-anti commutative supersymmetry can be described through a Cliffordization of the superspace fermionic coordinates. A NAC supersymmetric quantum mechanical model is shown to be a PT-symmetric Hamiltonian. (author)
Finding room for antilinear terms in the Hamiltonian
Eisele, Michael
2012-01-01
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system, another system can be constructed that is physically equivalent to the original one. It can be designed, despite the Wightman reconstruction theorem, so that antilinear operators in the original system become linear operators in the new system. Under certain conditions, these operators can then be added to the new Hamiltonian. The new quantum system has some unconventional features, a hidden degeneracy of the vacuum and a subtle distinction between the Hamiltonian and the observable of energy, but the physical equivalence guarantees that its states evolve like those in the original system and that corresponding measurements produce the same results. The same construction can be used to make time-reversal linear.
Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations
Ling CHEN
2011-01-01
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu's generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.
Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System
FANG Jian-Hui; YAN Xiang-Hong; LI Hong; CHEN Pei-Sheng
2004-01-01
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.
Hamiltonian replica-exchange in GROMACS: a flexible implementation
Bussi, Giovanni
2013-01-01
A simple and general implementation of Hamiltonian replica exchange for the popular molecular-dynamics software GROMACS is presented. In this implementation, arbitrarily different Hamiltonians can be used for the different replicas without incurring in any significant performance penalty. The implementation was validated on a simple toy model - alanine dipeptide in water - and applied to study the rearrangement of an RNA tetraloop, where it was used to compare recently proposed force-field co...
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables.
Applications of geometrical criteria for transition to Hamiltonian chaos.
Ben Zion, Yossi; Horwitz, Lawrence
2008-09-01
Using a recently developed geometrical method, we study the transition from order to chaos in an important class of Hamiltonian systems. We show agreement between this geometrical method and the surface of section technique applied to detect chaotic behavior. We give, as a particular illustration, detailed results for an important class of potentials obtained from the perturbation of an oscillator Hamiltonian by means of higher-order polynomials.
Applications of Noether conservation theorem to Hamiltonian systems
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
Applications of Noether conservation theorem to Hamiltonian systems
Mouchet, Amaury
2016-01-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
The Existence of Homoclinic Solutions for Second Order Hamiltonian System
Jie Gao
2011-10-01
Full Text Available The research of homoclinic orbits for Hamiltonian system is a classical problem, it has valuable applications in celestial mechanics, plasma physis, and biological engineering. For example, homoclinic orbits rupture can yield chaos lead to more complex dynamics behaviour. This paper studies the existence of homoclinic solutions for a class of second order Hamiltonian system, we will prove this system exists at least one nontrivial homoclinic solution.
Discrete-Time Models for Implicit Port-Hamiltonian Systems
Castaños, Fernando; Michalska, Hannah; Gromov, Dmitry; Hayward, Vincent
2015-01-01
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian sys...
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
FANHong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two panicles' relative coordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantum point-mass pendulum. The Hamiltonian displays the correct Schroedlnger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation are derived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
FAN Hong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two particles'relativecoordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantumpoint-mass pendulum. The Hamiltonian displays the correct Schrodinger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation arederived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Construction of alternative Hamiltonian structures for field equations
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems
XU Xi-Xiang; YANG Hong-Xiang; LU Rong-Wu
2008-01-01
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-fore matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.